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: 1

Answer

Point-slope form: $y-5 = 3(x-2)$ Slope-intercept form in function notation: $f(x)=3x-1$

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=3 and passes through the point (2, 5). This means that the point-slope form of the line's equation is: $y-5 = 3(x-2)$ Convert the equation to slope-intercept form by isolating $y$ to obtain: $y -5=3\cdot x- 3 \cdot 2 \\y-5 = 3x-6 \\y-5+5 = 3x-6+5 \\y = 3x - 1$ In function notation, the equation is: $f(x) = 3x - 1$
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