College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Cumulative Review - Page 197: 18



Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$ = slope and $b$ = y-intercept (2) The slope $m$ of the line that passes through the points $(x_1, y_1)$ 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: $m=\dfrac{-2-4}{2-(-1)} \\m=\dfrac{-6}{3} \\m=-2$ Substituting this for $m$ in the slope-intercept form gives: $y=-2x+b$ To find the value of $b$, substitute the x and y values of $(2, -2)$ to obtain: $y=-2x+b \\-2=-2(2)+b \\-2 = -4+b \\-2+4=b \\2=b$ Thus, the equation of the line that passes through the two given points is: $y=-2x+2$
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