Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 1 - Graphs - 1.3 Lines - 1.3 Assess Your Understanding - Page 31: 80


The slope is $m=\dfrac{1}{3}$. The y-intercept is $2$. The graph is attached below.

Work Step by Step

The slope of the line can be obtained by looking at the coefficient of $x$ in the slope-intercept form $y=mx+b$, where the coefficient of $x$ is the slope. $-x+3y=6$ $3y=x+6$ $y=\frac{x+6}{3}$ $y=\frac{1}{3}x+2$ Therefore the slope is $m=\frac{1}{3}$. At the y-intercept the x-coordinate of the point is $x=0$. Therefore we can calculate the y-coordinate by plugging 0 to $x$ in the equation: $-x+3y=6$ $0+3y=6$ $y=2$ The y-intercept is $2$.
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