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: 2


Point-slope form: $y-1=4(x-3)$ Slope-intercept form in function notation: $f(x) = 4x-11$

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) Slope-intercept form in function notation has the equation: $f(x) = mx + b$ where m= slope and b = y-intercept The given line has m=4 and passes through the point (3, 1). This means that the line's equation in point slope form is: $y-1 = 4(x-3)$ Convert the equation to slope-intercept form by isolating $y$ to obtain: $y -1=4(x-3) \\y-1=4\cdot x - 4\cdot 3 \\y-1 =4x-12 \\y-1+1=4x-12+1 \\y=4x-11$ In function notation, the slope-intercept form of the equation is: $f(x) = 4x -11$
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