Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.5 - The Point-Slope Form of the Equation of a Line - Exercise Set - Page 163: 5


Point-slope form: $y+2=-4(x+3)$ Function notation of the slope-intercept form: $f(x)=-4x-14$

Work Step by Step

RECALL: (i) The point-slope form of a line's equation is: $y-y_1=m(x-x_1)$ where m= slope and $(x_1, y_1)$ is a point on the line. (ii) The function notation of the slope-intercept form of a line's equation is: $f(x) = mx + b$ where m= slope and b = y-intercept The given line has $m=-4$ and passes through the point (-3, -2). This means that the point-slope form of the line's equation is: $y-(-2) = -4[x-(-3)] \\y+2=-4(x+3)$ Convert the equation to slope-intercept form by isolating $y$ to obtain: $y + 2 =-4(x+3) \\y+2=-4\cdot x + (-4)\cdot 3 \\y+2=-4x+(-12) \\y+2=-4x-12 \\y+2-2=-4x-12-2 \\y=-4x-14$ In function notation, the slope-intercept form of the equation is: $f(x) = -4x-14$
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