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: 9


Point-slope form: $y+\frac{1}{2} = -(x+2)$ Function notation of the slope-intercept form: $f(x) = -x -\frac{5}{2}$

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 $m=-1$ and passes through the point $(-2, -\frac{1}{2})$. This means that the point-slope form of the line's equation is: $y-(-\frac{1}{2}) = -1[x-(-2)] \\y+\frac{1}{2}=-(x+2)$ Convert the equation to slope-intercept form by isolating $y$ to obtain: $y + \frac{1}{2} =-(x+2) \\y+\frac{1}{2}=-1\cdot x + (-1)\cdot 2 \\y+\frac{1}{2}=-x+(-2) \\y+\frac{1}{2}=-x-2 \\y+\frac{1}{2}-\frac{1}{2}=-x-2-\frac{1}{2} \\y=-x -\frac{4}{2} - \frac{1}{2} \\y=-x-\frac{5}{2}$ In function notation, the slope-intercept form of the equation is: $f(x) = -x-\frac{5}{2}$
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