Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Summary Exercises - Finding Slopes and Equations of Lines: 14

Answer

(a) $y=\frac{2}{3}x+8$ (b) $2x-3y=-24$

Work Step by Step

A line in point-slope form has the equation: $y-y_1=m(x-x_1)$ We use the given point $(-3,6)$ and slope $m=2/3$: $y-y_{1}=m(x-x_{1})$ $y-6=\frac{2}{3}(x--3)$ $y-6=\frac{2}{3}(x+3)$ $y-6=\frac{2}{3}x+2$ $y=\frac{2}{3}x+8$ Now the line is in slope-intercept form ($y=mx+b$). (b) We convert to standard form ($Ax+By=C$): $y=\displaystyle \frac{2}{3}x+8$ $3*y=3(\displaystyle \frac{2}{3}x+8)$ $3y=2x+24$ $-2x+3y=24$ $2x-3y=-24$
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