Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 77


The slope of the line is $m=-\frac{A}{B}$ and the y-intercept is $b=\frac{C}{B}$.

Work Step by Step

Consider the following equation of a line: $Ax+By=C$ The slope-intercept form of a line with slope m and y intercept b is as follows: $y=mx+b$ Rearrange the equation in standard slope-intercept form of $y=mx+c$ by solving the equation for y. Bring all the variables other than y and constant terms to one side. $\begin{align} & Ax+By=C \\ & By=-Ax+C \end{align}$ Divide both sides by B to get, $\begin{align} & \frac{By}{B}=\frac{-Ax+C}{B} \\ & y=-\frac{A}{B}x+\frac{C}{B} \end{align}$ On comparing this equation $y=-\frac{A}{B}x+\frac{C}{B}$ with the slope–intercept form of a line $y=mx+b$, we can observe that $m=-\frac{A}{B}$ and the y-intercept is $b=\frac{C}{B}$. Hence, the slope of the line is $m=-\frac{A}{B}$ and the y-intercept is $b=\frac{C}{B}$.
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