Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises - Page 243: 42

Answer

slope: $=-\frac{1}{3}$ y-intercept: $(0, -3)$ Refer to the graph below.
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Work Step by Step

Solve for $y$: $x+3y=-9 \\x+3y-x=-9-x \\3y=-x-9 \\\frac{3y}{3}=\frac{-x-9}{3} \\y=-\frac{1}{3}x-3$ This means that the given equation is equivalent to $y=-\frac{1}{3}x-3$. RECALL: The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept. Thus, the equation $y=-\frac{1}{3}x-3$ has a slope of $-\frac{1}{3}$ and a y-intercept of $(0, -3)$. To graph the equation, perform the following steps: (1) Plot the y-intercept $(0, -3)$. (2) Use the slope to plot a second point. Since the slope is $-\frac{1}{3}$, from $(0, -3)$, move 1 unit down (the rise) and 3 units to the right (the run) to reach the point $(3,-4)$. Plot $(3. -4)$. (3) Connect the points using a straight line. (Refer to the graph in the answer part above)
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