Intermediate Algebra for College Students (7th Edition)

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

Chapter 2 - Review Exercises - Page 173: 35

Answer

The graph is shown in the image file.

Work Step by Step

The given equation of the line is $\Rightarrow x+2y=4$ Plug $y=0$ for the $x−$intercept. $\Rightarrow x+2(0)=4$ Simplify. $\Rightarrow x=4$ The $x−$intercept is $4$, so the line passes through $(4,0)$. Plug $x=0$ for the $y−$intercept. $\Rightarrow (0)+2y=4$ Simplify. $\Rightarrow 2y=4$ Divide both sides by $2$. $\Rightarrow \frac{2y}{2}=\frac{4}{2}$ Simplify. $\Rightarrow y=2$ The $y−$intercept is $2$, so the line passes through $(0,2)$. Checkpoint plug $x=2$. $\Rightarrow (2)+2y=4$ Simplify. $\Rightarrow 2+2y=4$ Subtract $2$ from both sides. $\Rightarrow 2+2y-2=4-2$ Simplify. $\Rightarrow 2y=2$ Divide both sides by $2$. $\Rightarrow \frac{2y}{2}=\frac{2}{2}$ $\Rightarrow y=1$ The checkpoint is (2,1). Plot the three points determines above. Draw a straight line through the points $(4,0)$ and $(0,2)$. We notice that the checkpoint $(2,1)$ also belongs to the line, therefore our graph is correct.
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