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: 67

Answer

$\color{blue}{y=-2x}$

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). The line we are looking for is perpendicular to $y=\frac{1}{2}x+4$ (whose slope is $\frac{1}{2}$). This means that line has a slope of $-2$ (since $-2(\frac{1}{2})=-1$). 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: $y=-2x+b \\-2 = -2(1)=b \\-2 = -2 + b \\-2+2=b \\0=b$ Thus, the equation of the line is: $y=-2x+0 \\\color{blue}{y=-2x}$
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