College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises - Page 113: 40



Work Step by Step

RECALL: (1) Perpendicular lines have slopes whose product is $-1$ (or negative reciprocal slopes). (2) The slope-intercept form of a line's equation is $y=mx+b$, where $m$ = slope and $b$ = y-intercept. The line is perpendicular to the line $y=-\dfrac{1}{2}x+7$ whose slope is $-\dfrac{1}{2}$. This means that slope of the line we are looking for is $2$ (the negative reciprocal of $-\frac{1}{2}$). Thus, the tentative equation of the line is: $y=2x+b$ The line passes through the point $(-3, 2)$. To find the value of $b$, substitute the x and y coordinates of this point into the tentative equation above to obtain: $y=2x+b \\2=2(-3) + b \\2 = -6 + b \\2+6 = b \\8=b$ Therefore, the equation of the line is $y=2x+8$.
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