Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises - Page 243: 20



Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept. (2) The slope $m$ of a line that contains the points $(x_1, y_2)$ and $(x_2, y_2)$ is given by the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$.. Solve for the slope using the formula in (2) above to obtain: $m=\dfrac{2-3}{-1-2}=\dfrac{-1}{-3}=\dfrac{1}{3}$ Thus, the tentative equation of the line is $y=\frac{1}{3}x+b$ To find the value of $b$, substitute the x and y values of one of the two given points to obtain: $y=\frac{1}{3}x+b \\3=\frac{1}{3}(2)+b \\3=\frac{2}{3}+b \\3-\frac{2}{3}=\frac{2}{3}+b-\frac{2}{3} \\\frac{9}{3}-\frac{2}{3}=b \\\frac{7}{3}=b$ Therefore, the equation of the line is $\color{blue}{y=\frac{1}{3}x+\frac{7}{3}}$.
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