Algebra 2 (1st Edition)

Published by McDougal Littell

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Mixed Review - Page 291: 75

Answer

The equation of the line is $y=2x+1$

Work Step by Step

$(x_{1},y_{1})=(2,5)$ $(x_{2},y_{2})=(4,9)$ Find the slope of the line: $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $m=\displaystyle \frac{9-5}{4-2}=\frac{4}{2}=2$ You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose $(x_{1},y_{1})=(2,5).$ $y-y_{1}=m(x-x_{1})\qquad$ ...substitute $5$ for $y_{1},\ 2$ for $m$ and $2$ for $x$. $y-5=2(x-2)\qquad$ ...apply the Distributive Property. $y-5=2x-4\qquad$ ...add $5$ to each side. $y=2x+1$

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