Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Entry-Level Assessment - Page xxxvii: 19



Work Step by Step

The slope-intercept equation for a line is $$y=mx+b$$ where $b$ is the y-intercept and the slope $m$ is given by $$m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$$ Here $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points on the line. Use $(-4,4)$ and $(2,-5)$ as the two points to find the slope as $$m=\frac{-5-4}{2-(-4)}=\frac{-9}{6}=\frac{-3}{2}$$ Substitute the coordinates of one of the points, say, $(-4,4)$, and $m=-3/2$ into the first equation $$4=(\frac{-3}{2})(-4) + b \\4=6+b$$ and solve for $b$ by subtracting $6$ on both sides of the equation: $$b=-2$$
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