Algebra 2 Common Core

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

Chapter 2 - Functions, Equations, and Graphs - Chapter Test - Page 127: 18

Answer

$y+6=-16(x+1)$

Work Step by Step

With the given points, $ (-1,-6)$ and $(-2,10),$ then \begin{align*} y_1&= -6 ,\\y_2&= 10 ,\\x_1&= -1 ,\text{ and }\\ x_2&= -2 .\end{align*} Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, the slope, $m,$ of the line connecting the two given points is \begin{align*} m&= \dfrac{-6-10}{-1-(-2)} \\\\&= \dfrac{-6-10}{-1+2} \\\\&= \dfrac{-16}{1} \\\\&= -16 .\end{align*} Using $ y-y_1=m(x-x_1) $ or the Point-Slope Form, with $m= -16 $ and using the point $ (-1,-6) $, then \begin{align*} y-(-6)&=-16(x-(-1)) \\ y+6&=-16(x+1) .\end{align*} A Point-Slope Form of the line with the given conditions is $ y+6=-16(x+1) .$
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