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: 50



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: $m=\dfrac{5-4}{2-(-3)}=\dfrac{1}{5}$ Using the point $(2, 5)$ and the slope $\frac{1}{5}$, the equation of the line can be written as: $y-5=\dfrac{1}{5}(x-2)\\ y-5=\dfrac{1}{5}x-\dfrac{2}{5}\\ y=\dfrac{1}{5}x-\dfrac{2}{5}+5\\ y=\dfrac{1}{5}x-\dfrac{2}{5}+\dfrac{25}{5}\\ y=\dfrac{1}{5}x+\dfrac{23}{5}\\ $
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