Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Cumulative Review Exercises - Page 251: 11

Answer

The graph is shown below.

Work Step by Step

The given equation of the line is $\Rightarrow f(x)=−\frac{2}{3}x+2$ let $f(x)=y$. $\Rightarrow y=−\frac{2}{3}x+2$ Plug $y=0$ for the $x−$intercept. $\Rightarrow 0=−\frac{2}{3}x+2$ Add $\frac{2}{3}x$ to both sides. $\Rightarrow 0+\frac{2}{3}x=−\frac{2}{3}x+2+\frac{2}{3}x$ Simplify. $\Rightarrow \frac{2}{3}x=2$ Isolate $x$. $\Rightarrow x=3$ The $x−$intercept is $3$, so the line passes through $(3,0)$. Plug $x=0$ for the $y−$intercept. $\Rightarrow y=−\frac{2}{3}(0)+2$ Simplify. $\Rightarrow y=2$ The $y−$intercept is $2$, so the line passes through $(0,2)$. Checkpoint plug $x=6$. $\Rightarrow y=−\frac{2}{3}(6)+2$ Simplify. $\Rightarrow y=−4+2$ $\Rightarrow y=−2$ The checkpoint is $(6,-2)$. Draw a straight line through these three points.
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