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: 49



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. Here, our line's slope can be calculated by the formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$, where the points $(x_1,y_1)$ and $(x_2,y_2)$ are on the line. We can plug in the given two points: $m=\dfrac{2-3}{-1-1}=\dfrac{-1}{-2}=\dfrac{1}{2}$ Using the point $(1, 3)$ and the slope $\frac{1}{02}$, the equation can be written as: $y-3=\dfrac{1}{2}(x-1)\\ y-3=\dfrac{1}{2}x-\dfrac{1}{2}\\ y=\dfrac{1}{2}x-\dfrac{1}{2}+3\\ y=\dfrac{1}{2}x+\dfrac{5}{2}$
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