## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 2 - Functions, Equations, and Graphs - 2-3 Linear Functions and Slope-Intercept Form - Practice and Problem-Solving Exercises - Page 79: 55

#### Answer

\begin{array}{l}\require{cancel} \\\text{Slope: } -\dfrac{A}{B} \\\text{$y$-intercept: } \left(0, \dfrac{C}{B}\right) \end{array}

#### Work Step by Step

Using the properties of equality, in the form $y=mx+b,$ the given equation is equivalent to: \begin{array}{l}\require{cancel} D\left( \dfrac{A}{D}x+\dfrac{B}{D}y \right)=\left( \dfrac{C}{D} \right)D \\\\ Ax+By=C \\\\ By=-Ax+C \\\\ \dfrac{By}{B}=\dfrac{-Ax+C}{B} \\\\ y=-\dfrac{A}{B}x+\dfrac{C}{B} .\end{array} Using $y=mx+b$ (where $m$ is the slope and $b$ is the $y$-intercept) or the Slope-Intercept Form of linear equations, then the equation above has the following properties \begin{array}{l}\require{cancel} \\\text{Slope: } -\dfrac{A}{B} \\\text{$y$-intercept: } \left(0, \dfrac{C}{B}\right) .\end{array}

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