Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 3 - Introduction to Graphing - 3.7 Point-Slope Form and Equations of Lines - 3.7 Exercise Set: 29

Answer

$y=x-32$

Work Step by Step

RECALL: (1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line. (2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$ is the y-coordinate of the line's y-intercept. (3) Parallel lines have equal slopes. (4) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). Write $x+y=18$ in slope-intercept form: $x+y=18 \\y=18-x \\y=-x+18$ This means the equation $x+y=18$ is equivalent to $y=-x+18$. The line is perpendicular to $y=-x+18$. Since the slope of this line is $-1$, then the slope of the line perpendicular to it is the negative reciprocal of $-1$, which is $1$. Using the given point on the line $(0, -32)$ (which is the y-intercept) and the slope $1$, the equation of the line in slope-intercept form is: $y=x+(-32) \\y=x-32$
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