Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 30: 43

Answer

$y-2=-\dfrac{1}{2}(x-1)$

Work Step by Step

The equation of a line in the point-slope form is the following: $y-y_1=m(x-x_1)$, where $m$ is the slope and the point $(x_1,y_1)$ is on the graph. In order to determine the equation of a line, we have to calculate the slope. For this, we can use the rule, that the product of the slopes of two perpendicular lines equals $-1$. Here, a perpendicular line is $y=2x$. In this form, the slope can be seen as the coefficient of $x$, which is $2$ Therefore our line's slope $m$ can be calculated as: $m\times2=-1$ $m=-\dfrac{1}{2}$ Therefore, using the point $(1, 2)$ and the slope $-\frac{1}{2}$, the equation can be written as: $y-2=-\dfrac{1}{2}(x-1)$
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