## Precalculus (10th Edition)

Published by Pearson

# Chapter 1 - Graphs - 1.3 Lines - 1.3 Assess Your Understanding - Page 31: 81

#### Answer

The slope is $m=\frac{2}{3}$. The $y$-intercept is $-2$. The graph is attached below.

#### Work Step by Step

Isolate $y$ to obtain: $2x-3y=6$ $-3y=-2x+6$ $y=\frac{2}{3}x-2$ In a line's equation in slope-intercept form, which is $y=mx+b$, the constant $b$ is the $y$-intercept while the coefficient of $x$, which is $m$, is the slope. Thus, in $y=\frac{2}{3}x-2$ we have: $y$-intercept is $-2$ slope=$m=\frac{2}{3}$. Plot the point $(0, -2)$. The slope is $\frac{2}{3}$ so from $(0, 2)$, move $3$ units to the right and $2$ units upward to have $(3, 0)$. Connect the points using a straight line.

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