Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 20


point-slope form: $y+\frac{1}{4}=-(x+4)$ slope-intercept form: $y=-x-4.25$

Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where m = slope and b = y-intercept (2) The point-slope form of a line's equation is: $y-y_1=m(x-x_1)$ (a) point-slope form The given line has a slope of $-1$ and passes through the point $(-4, -\frac{1}{4})$. Substitute these values into the point-slope form above to obtain: $y-(-\frac{1}{4})=-1[x-(-4)] \\y+\frac{1}{4} = -(x+4)$ (b) slope-intercept form Substitute the slope $-1$ to $m$ to obtain the tentative equation: $y=-x+b$ The line passes through $(-4, -\frac{1}{4})$. This means that the coordinates of this point satisfy the equation of the line. Substitute the x and y-coordinates of this point into the tentative equation to obtain: $y=-x+b \\-\frac{1}{4} = -(-4) + b \\-\frac{1}{4} = 4 + b \\-\frac{1}{4}-4= b \\-4.25 = b$ Thus, the equation of the line is $y=-x-4.25$.
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