Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.2 Linear Functions and Their Graphs - Exercise Set 7.2 - Page 430: 40

Answer

(a) $y=-\dfrac{5}{3}x+5$ (b) slope = $-\dfrac{5}{3}$, y-intercept = $5$ (c) Refer to the image below for the graph.

Work Step by Step

(a) The slope-intercept form is $y=mx+b$ where m = slope and b = y-intercept. Subtract $5x$ on both sides to obtain: $3y=15-5x \\3y=-5x+15$ Divide both sides by $3$ to obtain: $y=\dfrac{-5x+15}{3} \\y = -\dfrac{5}{3}x + 5$ (b) The equation has $m=-\dfrac{5}{3}$ and $b=5$. Thus, slope = $-\dfrac{5}{3}$ y-intercept = $5$ (c) Plot the y-intercept point $(0, 5)$. From $(0, 5)$, move 5 units down (the rise) and 3 units to the right (the run). These steps lead to the point $(3, 0)$. Connect the two points using a line to complete the graph.
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