College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding - Page 179: 70



Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$ = slope and $b$ = y-intercept (2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). Write the equation of the given line in slope-intercept method to obtain: $x-2y=-5 \\x+5=2y \\\frac{x+5}{2}=\frac{2y}{2} \\\frac{x}{2} + \frac{5}{2} = y \\y=\frac{1}{2}x+\frac{5}{2}$ The line we are looking for is perpendicular to the line above (whose slope is $\frac{1}{2}$). This means that the line has a slope of $-2$ (since $\frac{1}{2}(-2)=-1$). Thus, a tentative equation of the line we are looking for is: $y=-2x+b$ To find the value of $b$, substitute the x and y values of the given point to obtain: $y=-2x+b \\4 = -2(0)+b \\4=0+b \\4 =b$ Thus, the equation of the line is: $\color{blue}{y=-2x+4}$
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