Precalculus (6th Edition)

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

Chapter 2 - Graphs and Functions - Summary Exercises on Graphs, Circles, Functions, and Equations - Exercises - Page 248: 15


$\color{blue}{y=-\frac{2}{3}x}$ Refer to the graph below.

Work Step by Step

RECALL: (1) Parallel lines have the same slope. (2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the y-intercept. The line is parallel to $2x+3y=6$. Write this equation in slope-intercept form to find its slope. $2x+3y=6 \\3y=6-2x \\3y=-2x+6 \\\frac{3y}{3}=\frac{-2x+6}{3} \\y=-\frac{2}{3}x+2$ The line has a slope of $-\frac{2}{3}$. This means that the slope of the line parallel to it is also $-\frac{2}{3}$. Thus, the tentative equation of the line we are looking for is $y=-\frac{2}{3}$. To find the value of $b$, substitute the x and y values of the point $(-3, 2)$ to obtain: $y=-\frac{2}{3}x+b \\2=-\frac{2}{3}(-3)+b \\2=2+b \\2-2=b \\0=b$ Thus, the equation of the line is: $y=-\frac{2}{3}x+0 \\\color{blue}{y=-\frac{2}{3}x}$ Refer to the graph in the answer part above.
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