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: 13



Work Step by Step

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. The given line has a slope of $-\frac{3}{2}$ therefore the tentative equation of the line is $y=-\frac{3}{2}x+b$ To find the value of $b$, substitute the x and y values of the given point into the tentative equation above to obtain: $y=-\frac{3}{2}x+b \\4=-5(-\frac{3}{2})+b \\4=\frac{15}{2}+b \\4-\frac{15}{2}=\frac{15}{2}+b-\frac{15}{2} \\\frac{8}{2}-\frac{15}{2}=b \\-\frac{7}{2}=b$ Therefore, the equation of the line is $\color{blue}{y=-\frac{3}{2}x-\frac{7}{2}}$.
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