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: 4

Answer

Point-slope form: $y-1=8(x+4)$ Function form of the slope-intercept form: $f(x)=8x+33$

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=8 and passes through the point (-4, 1). This means that the point-slope form of the line's equation is: $y-1 = 8[x-(-4)] \\y-1=8(x+4)$ Convert the equation to slope-intercept form by isolating $y$ to obtain: $y - 1 =8(x+4) \\y-1=8\cdot x + 8\cdot 4 \\y-1 =8x+32 \\y-1+1=8x+32+1 \\y=8x+33$ In function notation, the slope-intercept form of the equation is: $f(x) = 8x+33$
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