Algebra 2 Common Core

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

Chapter 2 - Functions, Equations, and Graphs - Mid-Chapter Quiz - Page 89: 21



Work Step by Step

With the given points, $(-4,-3)\text{ and } (2,7),$ then \begin{align*} y_1&= -3 ,\\y_2&= 7 ,\\x_1&= -4 ,\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 is \begin{align*}\require{cancel} m&=\dfrac{-3-7}{-4-2} \\\\&= \dfrac{-10}{-6} \\\\&= \dfrac{\cancel{-10}^5}{\cancel{-6}^3} \\\\&= \dfrac{5}{3} .\end{align*} Using $ y-y_1=m(x-x_1) $ or the Point-Slope Form of linear equations, with the point $(-4,-3)$ and $m=\dfrac{5}{3},$ then \begin{align*} y-(-3)&=\dfrac{5}{3}(x-(-4)) \\\\ y+3&=\dfrac{5}{3}(x+4) .\end{align*} Hence, an equation of the line in Point-Slope Form is $ y+3=\dfrac{5}{3}(x+4) .$
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