Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 1 - Graphs - 1.3 Lines - 1.3 Assess Your Understanding - Page 31: 70



Work Step by Step

The slope of the line can be found as the product of the slopes of two perpendicular lines is $-1$. Hence, the product of the slope of the line $x-2y=-5$ and the one we are trying to find is equal to $-1$. The given line can be rewritten as: $y=\frac{1}{2}x+2.5$, in this form the coefficient of $x$ gives the slope. Thus, $m_1=\frac{1}{2}=0.5$ This means that the slope ($m_2$) of the line we are after can be found by having: $0.5\times m_2=-1$ $m_2=-2$, this is the slope of the line we are trying to find. If we have the slope and a point on the graph $(0,4)$ we can use the point-slope formula to calculate the equation of the line: $y-y_1=m(x-x_1)$ $y-4=-2(x-0)$ $y-4=-2x$ $y=-2x+4$
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