Informative line

# Relationship between Two Number Patterns

• A relation can be found between two patterns.
• There should be two patterns with a specific rule.

Consider the following example:

Generate two number patterns starting from zero using the given rules. Then compare and find the relationship between the two patterns.

(i) Add $$4$$

(ii) Add $$6$$

(i) There are two patterns as follows:

Pattern $$(1)$$ - Addition of $$4$$

Pattern $$(2)$$ - Addition of $$6$$

(ii) Starting from Zero,

$$0, \;4, \;8, \;12, \;16, \;20,...$$ [Pattern $$(1)$$ series]

$$0, \;6, \;12, \;18, \;24, \;30,...$$[Pattern $$(2)$$ series]

(iii) Write both number patterns in ordered pairs with corresponding terms.

$$(0, 0), \;(4, 6), \;(8, 12), \;(12, 18), \;(16, 24), \;(20, 30),.....$$

(iv) Try to find the relation between corresponding terms. Compare each pair, there are differences of $$0,\;2,\;4,\;6,\;8,\;10,....$$

This relation can be written as $$2n$$

where n = Whole number

#### Generate two number patterns starting from 2 using the given rules: (i) Multiply $$2$$ (ii) Add $$4$$  Compare both the patterns and find the difference between the $$5^{th}$$ terms of both the patterns.

A $$2$$

B $$4$$

C $$10$$

D $$14$$

×

### Generate two number patterns starting from 2 using the given rules: (i) Multiply $$2$$ (ii) Add $$4$$  Compare both the patterns and find the difference between the $$5^{th}$$ terms of both the patterns.

A

$$2$$

.

B

$$4$$

C

$$10$$

D

$$14$$

Option D is Correct

# Tables

• The relationship between dependent and independent variables can be represented with the help of a table.
 Independent Dependent Input Output
• A table that shows how a value changes according to a rule is known as input-output table.
• The independent variable is always in the left handside column, while the dependent variable is in the right handside column.
• The value of the output depends on

(i) the value of the input.

(ii) the rule.

• The rule shows the relationship between input and output.
• Tables can be used to represent an equation.

Consider an example: Make a table from the given equation: $$2x+1=y$$

• To make a table from the given rule, give inputs in the equation and get outputs.

$$2x+1=y$$

Put $$x=1$$, then $$2(1)+1=y$$

$$\Rightarrow\;2+1=y$$

$$\Rightarrow\;3=y$$

Put $$x=2$$, then $$2(2)+1=y$$

$$\Rightarrow4+1=y$$

$$\Rightarrow\;5=y$$

Put $$x=3$$, then $$2(3)+1=y$$

$$\Rightarrow\;6+1=y$$

$$\Rightarrow\;7=y$$

Put $$x=4$$, then $$2(4)+1=y$$

$$\Rightarrow\;8+1=y$$

$$\Rightarrow\;9=y$$

• Write inputs and outputs in ordered pairs in the form: (input, output)

$$(1,\;3),\;(2,\;5),\;(3,\;7),\;(4,\;9)$$

• Now, write inputs on the left side and outputs on the right side.
Input $$(x)$$ Output $$(y)$$
$$1$$ $$3$$
$$2$$ $$5$$
$$3$$ $$7$$
$$4$$ $$9$$

#### An equation is given: $$3x+4=y$$ Which option correctly represents the input-output table for the given equation?

A   $$x$$ $$y$$ 1 3 2 4 3 5

B     $$x$$ $$y$$ 1 7 2 8 3 9

C   $$x$$ $$y$$ 1 7 2 10 3 13

D   $$x$$ $$y$$ 1 1 2 2 3 3

×

The given equation is

$$3x+4=y$$

(i) Give inputs in the equation and get outputs.

Put $$x=1$$, then $$3(1)+4=y$$

$$\Rightarrow\;3+4=y$$

$$\Rightarrow\;7=y$$

Put $$x=2$$, then $$3(2)+4=y$$

$$\Rightarrow\;6+4=y$$

$$\Rightarrow\;10=y$$

Put $$x=3$$, then $$3(3)+4=y$$

$$\Rightarrow\;9+4=y$$

$$\Rightarrow\;13=y$$

(ii) Write inputs and outputs in ordered pairs in the form: (input, output).

$$(1,\;7)$$

$$(2,\;10)$$

$$(3,\;13)$$

Now, make a table from the ordered pairs.

$$x$$ $$y$$
1 7
2 10
3 13

Hence, option (C) is correct.

### An equation is given: $$3x+4=y$$ Which option correctly represents the input-output table for the given equation?

A

$$x$$ $$y$$
1 3
2 4
3 5
.

B

$$x$$ $$y$$
1 7
2 8
3 9

C

$$x$$ $$y$$
1 7
2 10
3 13

D

$$x$$ $$y$$
1 1
2 2
3 3

Option C is Correct

# Completion of Input-Output Table

• The relationship between dependent and independent variables can be represented with the help of a table.
 Independent Dependent Input Output

• A table that shows how a value changes according to a rule is known as the input-output table.
• The independent variable is always in the left hand side column, while the dependent variable is in the right hand side column.
• The value of the output depends on

(i) the value of the input.

(ii) the rule.

• The rule shows the relationship between input and output.
• Tables can be used to represent an equation.

Consider an example: Make a table from the given equation: $$2x+1=y$$

• To make a table from the given rule, give inputs in the equation and get outputs.

$$2x+1=y$$

Put $$x=1$$, then $$2(1)+1=y$$

$$\Rightarrow\;2+1=y$$

$$\Rightarrow\;3=y$$

Put $$x=2$$, then $$2(2)+1=y$$

$$\Rightarrow4+1=y$$

$$\Rightarrow\;5=y$$

Put $$x=3$$, then $$2(3)+1=y$$

$$\Rightarrow\;6+1=y$$

$$\Rightarrow\;7=y$$

Put $$x=4$$, then $$2(4)+1=y$$

$$\Rightarrow\;8+1=y$$

$$\Rightarrow\;9=y$$

• Write inputs and outputs in ordered pairs in the form: (input, output)

$$(1,\;3),\;(2,\;5),\;(3,\;7),\;(4,\;9)$$

• Now, write inputs on the left side and outputs on the right side.
Input$$(x)$$ Output $$(y)$$
$$1$$ $$3$$
$$2$$ $$5$$
$$3$$ $$7$$
$$4$$ $$9$$

#### Jacob has $$3$$ times less than $$10$$ candies as much as Marc has. They plot a table as shown. Which one of the following options represents the correctly completed table?          Number of candies $$x\;\text{(Marc)}$$ $$y\; \text {(Jacob)}$$           $$0$$            $$10$$           $$1$$             $$2$$              $$4$$           $$3$$

A $$\begin{array} {|c|c|} \hline x&y\\ \hline 0&10\\ \hline 1&\color{red}6\\ \hline 2&4\\ \hline 3&\color{red}1\\ \hline \end{array}$$

B $$\begin{array} {|c|c|}\hline x&y\\ \hline 0&10\\ \hline 1&\color{red}3\\ \hline 2&4\\ \hline 3&\color{red}5\\ \hline \end{array}$$

C $$\begin{array} {|c|c|}\hline x&y\\ \hline 0&10\\ \hline 1&\color{red}6\\ \hline 2&4\\ \hline 3&\color{red}2\\ \hline \end{array}$$

D $$\begin{array} {|c|c|} \hline x&y\\ \hline 0&10\\ \hline 1&\color{red}7\\ \hline 2&4\\ \hline 3&\color {red}1\\ \hline \end{array}$$

×

### Jacob has $$3$$ times less than $$10$$ candies as much as Marc has. They plot a table as shown. Which one of the following options represents the correctly completed table?          Number of candies $$x\;\text{(Marc)}$$ $$y\; \text {(Jacob)}$$           $$0$$            $$10$$           $$1$$             $$2$$              $$4$$           $$3$$

A

$$\begin{array} {|c|c|} \hline x&y\\ \hline 0&10\\ \hline 1&\color{red}6\\ \hline 2&4\\ \hline 3&\color{red}1\\ \hline \end{array}$$

.

B

$$\begin{array} {|c|c|}\hline x&y\\ \hline 0&10\\ \hline 1&\color{red}3\\ \hline 2&4\\ \hline 3&\color{red}5\\ \hline \end{array}$$

C

$$\begin{array} {|c|c|}\hline x&y\\ \hline 0&10\\ \hline 1&\color{red}6\\ \hline 2&4\\ \hline 3&\color{red}2\\ \hline \end{array}$$

D

$$\begin{array} {|c|c|} \hline x&y\\ \hline 0&10\\ \hline 1&\color{red}7\\ \hline 2&4\\ \hline 3&\color {red}1\\ \hline \end{array}$$

Option D is Correct

# Linear or Non-linear Graphs

• A graph can be linear or non-linear.
• When the solution of an equation on a graph forms a straight line, it is called a linear graph.

For example: Consider the graph shown.

Here, the solution of an equation forms a straight line so, it is a linear graph.

When the solution of an equation on a graph does not form a straight line, it is called a non-linear graph.

For example: Consider the graph shown.

Here, the solution of an equation forms a zig-zag line so, it is a non-linear graph.

Steps to identify linear or non-linear relationship:

(i) Plot the coordinates on the graph.

(ii) Connect the points through lines.

If the solution makes a straight line, it is a linear relationship and if it does not, it is a non-linear relationship.

• Relationship represents the relation between $$x$$ and $$y$$, and shows how dependent variable changes according to the independent variable.

A

B

C

D

×

### Which one of the following graphs represents the linear relationship?

A
B
C
D

Option D is Correct

# Real Life Examples to Represent through Table

• Equations and tables can also be used to represent real life information, mathematically.

Consider an example:

Taylor is going for horse riding.

The riding charge is $$7/hr$$.

• Let $$h$$ represents the number of hours of riding and $$c$$ represents the total cost.

Equation is $$c=7h$$

To make a table from the equation, give inputs to get outputs.

If $$h=1$$, then $$c=7×1$$

$$\Rightarrow\;c=7$$

If $$h=2$$, then $$c=7×2$$

$$\Rightarrow\;c=14$$

If $$h=3$$, then $$c=7×3$$

$$\Rightarrow\;c=21$$

If $$h=4$$, then $$c=7×4$$

$$\Rightarrow\;28$$

Write in ordered pairs: $$(1,7),\,(2,14),\,(3,21),\,(4,28)$$

 Hours (h) Cost (c) 1 7 2 14 3 21 4 28

#### Emma's age is twice the age of Cody. Which one correctly represents the relationship between Emma and Cody's ages?

A     Cody ($$C$$) Emma ($$E$$) 10 20 11 22 12 24 13 26

B   Cody ($$C$$) Emma ($$E$$) 10 11 11 12 12 13 13 14

C   Cody ($$C$$) Emma ($$E$$) 10 12 11 13 12 14 13 15

D   Cody ($$C$$) Emma ($$E$$) 10 13 11 15 12 30 13 25

×

### Emma's age is twice the age of Cody. Which one correctly represents the relationship between Emma and Cody's ages?

A

 Cody ($$C$$) Emma ($$E$$) 10 20 11 22 12 24 13 26

.

B

 Cody ($$C$$) Emma ($$E$$) 10 11 11 12 12 13 13 14

C

 Cody ($$C$$) Emma ($$E$$) 10 12 11 13 12 14 13 15

D

 Cody ($$C$$) Emma ($$E$$) 10 13 11 15 12 30 13 25

Option A is Correct

# Graphing Equations

• Equations and tables can also be graphed to represent a real-life situation.
• We can represent an equation by graphical method.
• If we have an equation in terms of two variables and there is a dependent and an independent variable, then we can plot a graph between them.
• A graph shows the relationship between two quantities in the form of increment and decrement.

When graphing:

(i) The independent variable is always across the $$x-$$axis.

(ii) The dependent variable is always up the $$y-$$axis.

Steps for graphing equations:

(i) Write an equation to represent the situation.

(ii) Make an input-output table from the equation.

(iii) Once we have the equation, we can write coordinates in the form: (independent variable, dependent variable)

Coordinates: A pair of values that shows an exact position on a coordinate plane.

(iv) Plot the coordinates of the equation on the graph.

For example: A bakery shopkeeper makes cookies. The table shows the relationship between the time in hours $$(x)$$ and the number of cookies the shopkeeper makes $$(y)$$.

• We can write an equation from the given table.

$$\begin{array} {|c|c|} \hline (x)&(y)\\ \text{(In hours)}&\text{(Number of cookies)}\\ \hline 1&20\\ \hline 2&40\\ \hline 3&60\\ \hline 4&80\\ \hline \end{array}$$

• The equation for the situation is, $$y=20x$$
• Thus, $$20$$ cookies are being made each hour.

• The value of $$y$$ depends upon the value of $$x.$$

Hence, $$y$$ (the number of cookies) is the dependent variable.

$$x$$ (the time in hours) is the independent variable.

• Now, write coordinates from the given table.

$$\begin{array} {|c|c|} \hline (x)&(y)&\text{Coordinates}\\ &&(x,\,y)\\ \hline 1&20&(1,\;20)\\ \hline 2&40&(2,\;40)\\ \hline 3&60&(3,\;60)\\ \hline 4&80&(4,\;80)\\ \hline \end{array}$$

• Plot the coordinates on the graph from the table.
• From this plotted graph, we can observe the relation between $$x$$ and $$y.$$
• If one value increases, the other value also increases.

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<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 96 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 A Notice (8): Undefined offset: 0 [APP/View/Elements/theorypage.ctp, line 111]Code Context <div class="col-md-6">   <div class="col-sm-6">   <p><span id="ring-brd" class="col-xs-2">A</span> <span><?php echo strip_tags($bucketData[$i]['Bucket']['QuestionOption'][0]['QuestionOption']['description']); ?></span> $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
$subjectUrl = 'grade-6-maths'$subjectdataHeader = array(
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 111 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 Notice (8): Undefined offset: 0 [APP/View/Elements/theorypage.ctp, line 115]Code Context   <?php   if(trim($bucketData[$i]['Bucket']['QuestionOption'][0]['QuestionOption']['image'])!=''){ $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
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<li>Plot the coordinates on the graph from the table.</li>
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<li>Plot the coordinates on the graph from the table.</li>
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=> '3', 'name' => 'Level 5', 'position' => '5', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ) )$description = null
$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
$subjectUrl = 'grade-6-maths'$subjectdataHeader = array(
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'Subject' => array(
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(int) 5 => array(
'Subject' => array(
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 145 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 Notice (8): Undefined offset: 2 [APP/View/Elements/theorypage.ctp, line 148]Code Context   <?php   if(trim($bucketData[$i]['Bucket']['QuestionOption'][2]['QuestionOption']['image'])!=''){ $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ) ) ), (int) 6 => array( 'Bucket' => array( 'id' => '2066', 'topic_id' => '467', 'level_id' => '5', 'goal_id' => '2', 'name' => 'Bucket25467', 'question_id' => '10026', 'standard_time' => '120', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '73', 'admin_two' => '51', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 8, 'bucket' => 'Bucket 8', 'Question' => array( [maximum depth reached] ), 'QuestionOption' => array( [maximum depth reached] ), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '5', 'module_id' => '3', 'name' => 'Level 5', 'position' => '5', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ) )$description = null
$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 148 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 D Notice (8): Undefined offset: 3 [APP/View/Elements/theorypage.ctp, line 161]Code Context   <div class="col-sm-6">   <p><span id="ring-brd" class="col-xs-2">D</span> <span><?php echo strip_tags($bucketData[$i]['Bucket']['QuestionOption'][3]['QuestionOption']['description']); ?></span> $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
$subjectUrl = 'grade-6-maths'$subjectdataHeader = array(
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$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 165 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 × ### Notice (8): Undefined index: Question [APP/View/Elements/theorypage.ctp, line 222]Code Context <div class="col-xs-12 options-in-sol">   <div class="col-md-8 solSteps">   <h3><span class="fa fa-question-circle-o"></span> <?php echo 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), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '1', 'name' => 'Goal 1', 'position' => '1', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ) ) ), (int) 3 => array( 'Bucket' => array( 'id' => '2069', 'topic_id' => '467', 'level_id' => '5', 'goal_id' => '1', 'name' => 'Bucket15467', 'question_id' => '10030', 'standard_time' => '120', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '73', 'admin_two' => '51', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 6, 'bucket' => 'Bucket 6', 'Question' => array( [maximum depth reached] ), 'QuestionOption' => array( [maximum depth reached] ), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '5', 'module_id' => '3', 'name' => 'Level 5', 'position' => '5', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '1', 'name' => 'Goal 1', 'position' => '1', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ), (int) 4 => array( 'Bucket' => array( 'id' => '2062', 'topic_id' => '467', 'level_id' => '2', 'goal_id' => '2', 'name' => 'Bucket22467', 'question_id' => '10009', 'standard_time' => '30', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '51', 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'level_id' => '4', 'goal_id' => '2', 'name' => 'Bucket24467', 'question_id' => '10025', 'standard_time' => '75', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '35', 'admin_two' => '73', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 7, 'bucket' => 'Bucket 7', 'Question' => array([maximum depth reached]), 'QuestionOption' => array([maximum depth reached]), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '4', 'module_id' => '3', 'name' => 'Level 4', 'position' => '4', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ) ) ), (int) 6 => array( 'Bucket' => array( 'id' => '2066', 'topic_id' => '467', 'level_id' => '5', 'goal_id' => '2', 'name' => 'Bucket25467', 'question_id' => '10026', 'standard_time' => '120', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '73', 'admin_two' => '51', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 8, 'bucket' => 'Bucket 8', 'Question' => array( [maximum depth reached] ), 'QuestionOption' => array( [maximum depth reached] ), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '5', 'module_id' => '3', 'name' => 'Level 5', 'position' => '5', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ) )$description = null $SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths' $subjectUrl = 'grade-6-maths'$subjectdataHeader = array( (int) 0 => array( 'Subject' => array( 'id' => '6', 'name' => 'Calculus 1', 'short_display_name' => 'Differentiation', 'position' => '1', 'status' => '1', 'is_deleted' => '0' ), 'Chapter' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ), (int) 4 => array( [maximum depth reached] ) ) ), (int) 1 => array( 'Subject' => array( 'id' => '7', 'name' => 'Calculus 2', 'short_display_name' => 'Integration', 'position' => '2', 'status' => '1', 'is_deleted' => '0' ), 'Chapter' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ), (int) 4 => array( [maximum depth reached] ) ) ), (int) 2 => array( 'Subject' => array( 'id' => '3', 'name' => 'College Physics 1', 'short_display_name' => 'Mechanics', 'position' => '3', 'status' => '1', 'is_deleted' => '0' ), 'Chapter' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ), (int) 4 => array( [maximum depth reached] ) ) ), (int) 3 => array( 'Subject' => array( 'id' => '5', 'name' => 'College Physics 2', 'short_display_name' => 'Electrodynamics', 'position' => '4', 'status' => '1', 'is_deleted' => '0' ), 'Chapter' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ) ) ), (int) 4 => array( 'Subject' => array( 'id' => '9', 'name' => 'Grade 6 Maths', 'short_display_name' => 'maths 1', 'position' => '5', 'status' => '1', 'is_deleted' => '0' ), 'Chapter' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ), (int) 4 => array( [maximum depth reached] ), (int) 5 => array( [maximum depth reached] ) ) ), (int) 5 => array( 'Subject' => array( 'id' => '10', 'name' => 'Grade 7 Maths Algebra', 'short_display_name' => 'G-7 Algebra', 'position' => '6', 'status' => '1', 'is_deleted' => '0' ), 'Chapter' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ) ) $url = 'https://www.actucation.com/'$i = (int) 5 $j = (int) 4$str = '<ul> <li>Plot the coordinates on the graph from the table.</li> <li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li> <li>If one value increases, the other value also increases.</li> </ul> ' $pos = false$pos2 = false $header = ''$m = (int) 0 $correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 222 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 Notice (8): Undefined index: Question [APP/View/Elements/theorypage.ctp, line 224]Code Context <h3><span class="fa fa-question-circle-o"></span> <?php echo strip_tags($bucketData[$i]['Bucket']['Question']['Question']['question']); ?></h3>   <?php   if(trim($bucketData[$i]['Bucket']['Question']['Question']['image'])!=''){ $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
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<li>Plot the coordinates on the graph from the table.</li>
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
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$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 254 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 Notice (8): Undefined offset: 1 [APP/View/Elements/theorypage.ctp, line 259]Code Context <?php   }   if(trim($bucketData[$i]['Bucket']['QuestionOption'][1]['QuestionOption']['image'])!=''){ $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
$subjectUrl = 'grade-6-maths'$subjectdataHeader = array(
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 259 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::_renderElement() - CORE/Cake/View/View.php, line 1195 View::element() - CORE/Cake/View/View.php, line 412 include - APP/View/Students/subject.ctp, line 10 View::_evaluate() - CORE/Cake/View/View.php, line 935 View::_render() - CORE/Cake/View/View.php, line 897 View::render() - CORE/Cake/View/View.php, line 466 Controller::render() - CORE/Cake/Controller/Controller.php, line 952 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160 [main] - APP/webroot/index.php, line 327 Notice (8): Undefined offset: 2 [APP/View/Elements/theorypage.ctp, line 268]"> C Notice (8): Undefined offset: 2 [APP/View/Elements/theorypage.ctp, line 271]Code Context <span class="col-xs-1 span-design">C</span>   <?php   if(trim($bucketData[$i]['Bucket']['QuestionOption'][2]['QuestionOption']['description'])!=''){ $viewFile = '/home/bo6uxs8yrzio/public_html/app/View/Elements/theorypage.ctp'
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$url = 'https://www.actucation.com/'$i = (int) 5
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<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
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</ul>
'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
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$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
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array( 'id' => '4', 'module_id' => '3', 'name' => 'Level 4', 'position' => '4', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '1', 'name' => 'Goal 1', 'position' => '1', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ) ) ), (int) 3 => array( 'Bucket' => array( 'id' => '2069', 'topic_id' => '467', 'level_id' => '5', 'goal_id' => '1', 'name' => 'Bucket15467', 'question_id' => '10030', 'standard_time' => '120', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '73', 'admin_two' => '51', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 6, 'bucket' => 'Bucket 6', 'Question' => array( [maximum depth reached] ), 'QuestionOption' => array( [maximum depth reached] ), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '5', 'module_id' => '3', 'name' => 'Level 5', 'position' => '5', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '1', 'name' => 'Goal 1', 'position' => '1', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ), (int) 4 => array( 'Bucket' => array( 'id' => '2062', 'topic_id' => '467', 'level_id' => '2', 'goal_id' => '2', 'name' => 'Bucket22467', 'question_id' => '10009', 'standard_time' => '30', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '51', 'admin_two' => '34', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 3, 'bucket' => 'Bucket 3', 'Question' => array( [maximum depth reached] ), 'QuestionOption' => array( [maximum depth reached] ), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '2', 'module_id' => '2', 'name' => 'Level 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ) ) ), (int) 5 => array( 'Bucket' => array( 'id' => '2065', 'topic_id' => '467', 'level_id' => '4', 'goal_id' => '2', 'name' => 'Bucket24467', 'question_id' => '10025', 'standard_time' => '75', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '35', 'admin_two' => '73', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 7, 'bucket' => 'Bucket 7', 'Question' => array([maximum depth reached]), 'QuestionOption' => array([maximum depth reached]), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '4', 'module_id' => '3', 'name' => 'Level 4', 'position' => '4', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ), (int) 3 => array( [maximum depth reached] ) ) ), (int) 6 => array( 'Bucket' => array( 'id' => '2066', 'topic_id' => '467', 'level_id' => '5', 'goal_id' => '2', 'name' => 'Bucket25467', 'question_id' => '10026', 'standard_time' => '120', 'is_theory' => '1', 'is_hint' => '1', 'status' => '1', 'admin_one' => '73', 'admin_two' => '51', 'admin_three' => null, 'publish' => '1', 'duplicate' => '0', 'is_deleted' => '0', 'old_bucket_id' => '0', 'bucketname' => (int) 8, 'bucket' => 'Bucket 8', 'Question' => array( [maximum depth reached] ), 'QuestionOption' => array( [maximum depth reached] ), 'Solution' => array([maximum depth reached]) ), 'Level' => array( 'id' => '5', 'module_id' => '3', 'name' => 'Level 5', 'position' => '5', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Topic' => array( 'id' => '467', 'chapter_id' => '51', 'parent_id' => '541', 'name' => 'Relationship between Variables ', 'is_paid' => '0', 'price' => '0.00', 'pre_request' => '', 'position' => '3', 'status' => '1', 'publish' => '1', 'is_deleted' => '0' ), 'Goal' => array( 'id' => '2', 'name' => 'Goal 2', 'position' => '2', 'status' => '1', 'created' => '0', 'updated' => '0' ), 'Theory' => array( (int) 0 => array( [maximum depth reached] ), (int) 1 => array( [maximum depth reached] ), (int) 2 => array( [maximum depth reached] ) ) ) )$description = null
$SubtopicName = 'relationship between variables '$subject = 'Grade 6 Maths'
$subjectUrl = 'grade-6-maths'$subjectdataHeader = array(
(int) 0 => array(
'Subject' => array(
'id' => '6',
'name' => 'Calculus 1',
'short_display_name' => 'Differentiation',
'position' => '1',
'status' => '1',
'is_deleted' => '0'
),
'Chapter' => array(
(int) 0 => array(
[maximum depth reached]
),
(int) 1 => array(
[maximum depth reached]
),
(int) 2 => array(
[maximum depth reached]
),
(int) 3 => array(
[maximum depth reached]
),
(int) 4 => array(
[maximum depth reached]
)
)
),
(int) 1 => array(
'Subject' => array(
'id' => '7',
'name' => 'Calculus 2',
'short_display_name' => 'Integration',
'position' => '2',
'status' => '1',
'is_deleted' => '0'
),
'Chapter' => array(
(int) 0 => array(
[maximum depth reached]
),
(int) 1 => array(
[maximum depth reached]
),
(int) 2 => array(
[maximum depth reached]
),
(int) 3 => array(
[maximum depth reached]
),
(int) 4 => array(
[maximum depth reached]
)
)
),
(int) 2 => array(
'Subject' => array(
'id' => '3',
'name' => 'College Physics 1',
'short_display_name' => 'Mechanics',
'position' => '3',
'status' => '1',
'is_deleted' => '0'
),
'Chapter' => array(
(int) 0 => array(
[maximum depth reached]
),
(int) 1 => array(
[maximum depth reached]
),
(int) 2 => array(
[maximum depth reached]
),
(int) 3 => array(
[maximum depth reached]
),
(int) 4 => array(
[maximum depth reached]
)
)
),
(int) 3 => array(
'Subject' => array(
'id' => '5',
'name' => 'College Physics 2',
'short_display_name' => 'Electrodynamics',
'position' => '4',
'status' => '1',
'is_deleted' => '0'
),
'Chapter' => array(
(int) 0 => array(
[maximum depth reached]
),
(int) 1 => array(
[maximum depth reached]
),
(int) 2 => array(
[maximum depth reached]
),
(int) 3 => array(
[maximum depth reached]
)
)
),
(int) 4 => array(
'Subject' => array(
'id' => '9',
'short_display_name' => 'maths 1',
'position' => '5',
'status' => '1',
'is_deleted' => '0'
),
'Chapter' => array(
(int) 0 => array(
[maximum depth reached]
),
(int) 1 => array(
[maximum depth reached]
),
(int) 2 => array(
[maximum depth reached]
),
(int) 3 => array(
[maximum depth reached]
),
(int) 4 => array(
[maximum depth reached]
),
(int) 5 => array(
[maximum depth reached]
)
)
),
(int) 5 => array(
'Subject' => array(
'id' => '10',
'name' => 'Grade 7 Maths Algebra',
'short_display_name' => 'G-7 Algebra',
'position' => '6',
'status' => '1',
'is_deleted' => '0'
),
'Chapter' => array(
(int) 0 => array(
[maximum depth reached]
),
(int) 1 => array(
[maximum depth reached]
),
(int) 2 => array(
[maximum depth reached]
)
)
)
)
$url = 'https://www.actucation.com/'$i = (int) 5
$j = (int) 4$str = '<ul>
<li>Plot the coordinates on the graph from the table.</li>
<li>From this plotted graph, we can observe the relation between&nbsp;<span class="math-tex">$$x$$</span>&nbsp;and&nbsp;<span class="math-tex">$$y.$$</span></li>
<li>If one value increases, the other value also increases.</li>
</ul>
'
$pos = false$pos2 = false
$header = ''$m = (int) 0
\$correctOption = 'A'include - APP/View/Elements/theorypage.ctp, line 296
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::_renderElement() - CORE/Cake/View/View.php, line 1195
View::element() - CORE/Cake/View/View.php, line 412
include - APP/View/Students/subject.ctp, line 10
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::render() - CORE/Cake/View/View.php, line 466
Controller::render() - CORE/Cake/Controller/Controller.php, line 952
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160
[main] - APP/webroot/index.php, line 327

Option A is Correct

# Writing an Equation for a Given Graph

• A graph shows the relationship between two variables.
• This relation can be defined through an equation mathematically.
• Relation could be found by observing the curve of the graph, whether increasing or decreasing.

To write an equation from a given graph, following steps should be followed:

(i) Write the coordinates from the given graph.

(ii) Try to observe the relation between the coordinate pairs.

(iii) Write the relation in an equation form.

For example:

The following graph shows the relationship between the number of miles traveled and the number of hours.

• Write coordinates $$(x,\;y)$$ from the given graph:

$$(2,\;10)\\ (4,\;20)\\ (6,\;30)$$

• Try to find the relation between the pairs.

The first coordinate is, $$(2,\;10)$$

Here, $$2$$ is multiplied with $$5$$ to get $$10$$.

The second coordinate is, $$(4,\;20)$$

$$4$$ is multiplied with $$5$$ to get $$20$$.

The third coordinate is $$(6,\;30)$$

$$6$$ is multiplied with $$5$$ to get $$30$$.

So, we can write a rule: $$y=5x$$

• We will check to be sure that our rule is working or not.

$$y=5x$$

Put $$x=1$$, then $$y=5×1=5$$

Put $$x=2$$, then  $$y=5×2=10$$

Put $$x=3$$, then $$y=5×3=15$$ and so on.

It means our rule is working.

• So, $$y=5x$$ is the required equation.
• After finding the rule for the graph, we can get next coordinates.
• We can use trial and error method also, to find the rule for the graph from the given options.

#### Which one of the following rule is correct for the given graph?

A $$y=10+x$$

B $$y=2x$$

C $$y=x+20$$

D $$y=20x$$

×

### Which one of the following rule is correct for the given graph?

A

$$y=10+x$$

.

B

$$y=2x$$

C

$$y=x+20$$

D

$$y=20x$$

Option D is Correct