Free Study Material

NCERT Solutions

NCERT Books

Revision Notes

Practice Problems

This is one of our many quizzes on Graphing absolute value equations. Click on this to access more such competitive quizzes on Linear Inequalities.

Graphing absolute value equations Quiz 2

mathematics

 Find the equation of the given graph: $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/5eee95df-a456-4713-b2b2-d1adaed7a7aa8345873138034036084.png"/>

 Take any value of $x$ or $y$ from the graph and put that value in the equation you will get the answer and see which equation satisfies the value.

Take any value from the graph. Let's take $x = 1$ $ \\ $ Substitute this value in every given equation and see which equation gives $y = 2$ as we can see $(1,2)$ is plotted on the graph. $ \\ $  Putting $x = 1$ in option $(a)$ we get  $ \\  \left|7(1) - 3\right| = 2y  \\  \Rightarrow \left|4\right| = 2y  \\  \Rightarrow y = 2  \\ $ 

 Find the graph of the equation $\left|8x + 4\right| - \left|3x\right| = 3y$.

 Find the value of y at $x = 1$you will get the answer.

Put $x = 1$ in the given equation we get: $ \\  \left|8(1) + 4\right| - \left|3(1)\right| = 3y  \\  \Rightarrow 12 - 3 = 3y  \\  \Rightarrow 9 = 3y  \\  \Rightarrow y = 3  \\ $ So at $x = 1$ we get $y = 3$ now check which of the given graph located on $(1,3)$ $ \\ $ This argument can only be found on the third graph.

 Find the equation of the following graph: $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/98c52523-a4d5-4606-99bf-31a8593c8ac16044942820211019296.png"/>

 Let’s take $x = 2$ substitute this value in every given equation and see which equation gives $y = 5$ as the points plotted on the graph is $(2,5)$. $ \\ $ Putting $x = 2$ in option a we get,  $ \\ \left|4(2) + 3\right| - \left|\dfrac{1}{2}(2)\right| = 2y  \\   \Rightarrow 11 - 1 = 2y  \\   \Rightarrow y = 5  \\ $

 Find the correct equation of the following graph: $ \\ $  <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/75314005-eaed-468d-ae76-1f026d2187398132125344005793166.png"/>

Let’s take $x = 1$ substituting this value in every given equation and see which equation gives $y = 1.5$ as the points plotted are $(1,1.5)$ $ \\ $ Putting $x = 1$ in option $(b)$ we get, $ \\   \dfrac{1}{4}\left|8(1) - 3\right| - \left|\dfrac{1}{2}(1)\right| = \dfrac{1}{2}y  \\  \Rightarrow \dfrac{5}{4} - \dfrac{1}{2} = \dfrac{1}{2}y  \\  \Rightarrow \dfrac{{5 - 2}}{4} = \dfrac{1}{2}y  \\ \Rightarrow y = \dfrac{3}{4} \times 2 = 1.5  \\ $

 Find the equation of this graph: $ \\ $  <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/d16b9432-c50e-49fb-8a5c-bf8e3dedb7e61794568847080293617.png"/>

Let’s take $x = 2$ Now put this value in every given equation and see which equation gives $y = 4.5$as we can see $(2,4.5)$ is a plotted on the graph. $ \\ $ Putting $x = 2$ in option $(b)$ we get $ \\ \dfrac{1}{2}\left|8{(2)^2} - 3(2) + 4\right| - \left|3(2)\right| = 2y  \\  \Rightarrow \dfrac{1}{2}\left|32 - 6 + 4\right| - 6 = 2y  \\  \Rightarrow 2y = \dfrac{1}{2}(30) - 6  \\ \Rightarrow 2y = 15 - 6  \\ \Rightarrow y = 4.5  \\ $