## College Algebra (10th Edition)

Published by Pearson

# Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding: 81

#### Answer

$\text{slope}=m=\frac{2}{3}; \\\text{y-intercept}=b=-2$ Refer to the image below for the graph.

#### Work Step by Step

RECALL: The slope-intercept form of a line's equation is: $y=mx+b$ where $m$ = slope and $b$ = y-intercept Write the given equation in slope-intercept form by isolating $y$ on one side to obtain: $2x-3y=6 \\-3y = -2x+6 \\y=\frac{-2x+6}{-3} \\y = \frac{2}{3}x-2$ The equation above has: $\text{slope}=m=\frac{2}{3}; \\\text{y-intercept}=b=-2$ To graph the line, perform the following steps: (1) Plot the y-intercept point $(0, -2)$. (2) Use the slope $\frac{2}{3}$ to find another point on the line. From $(0, -2)$, move up 2 units (the rise) and move 3 units to the right (the run) to arrive at the point $(3, 0)$. (3) Complete the graph by connecting the two points using a straight line. (refer to the attached image in the answer part above for the graph)

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