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 - Page 218: 26



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). The line is perpendicular to $y=\frac{5}{8}x-2$. Since the slope of this line is $\frac{5}{8}$, then the slope of the line perpendicular to it is the negative reciprocal of $\frac{5}{8}$, which is $-\frac{8}{5}$. Using the given point on the line $(0, 9)$ (which is the y-intercept) and the slope $-\frac{8}{5}$, the equation of the line in slope-intercept form is: $y=-\frac{8}{5}x+9$
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