## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 2 - Review Exercises: 6

#### Answer

$x\text{-intercept: } \left( 8,0 \right) \\y\text{-intercept: } (0,-2)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of intercepts to find the $x$- and $y$-intercepts of the given equation, $x-4y=8 .$ Then plot the points corresponding to the intercepts and connect these with a line to get the graph. $\bf{\text{Solution Details:}}$ The $x$-intercept is the value of $x$ when $y=0.$ Substituting $y=0$ in the given equation, then \begin{array}{l}\require{cancel} x-4y=8 \\\\ x-4(0)=8 \\\\ x-0=8 \\\\ x=8 .\end{array} Hence, the $x$-intercept is $\left( 8,0 \right) .$ The $y$-intercept is the value of $y$ when $x=0.$ Substituting $x=0$ in the given equation, then \begin{array}{l}\require{cancel} x-4y=8 \\\\ 0-4y=8 \\\\ -4y=8 \\\\ y=\dfrac{8}{-4} \\\\ y=-2 .\end{array} Hence, the $y$-intercept is $(0,-2) .$ Connecting the following intercepts, \begin{array}{l}\require{cancel} x\text{-intercept: } \left( 8,0 \right) \\y\text{-intercept: } (0,-2) ,\end{array} gives the graph of the given equation.

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