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: 6

Answer

Point-slope form: $y+4=-6(x+2)$ Function notation of the slope-intercept form: $f(x) = -6x-16$

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 $m=-6$ and passes through the point (-2, -4). This means that the point-slope form of the line's equation is: $y-(-4) = -6[x-(-2)] \\y+4=-6(x+2)$ Convert the equation to slope-intercept form by isolating $y$ to obtain: $y +4 =-6(x+2) \\y+4=-6\cdot x + (-6)\cdot 2 \\y+4=-6x+(-12) \\y+4=-6x-12 \\y+4-4=-6x-12-4 \\y=-6x-16$ In function notation, the slope-intercept form of the equation is: $f(x) = -6x-16$
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