Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.10 - Lines - 1.10 Exercises - Page 114: 22

Answer

$y=-\frac{4}{3}x-4$

Work Step by Step

RECALL: (i) The y-intercept is the y-coordinate of the point where a line passes through the y-axis. (ii) The slope-intercept form of the equation of a line is: $y=mx+b$ where m=slope b=y-intercept The given line passes through the y-axis at $(0, -4)$ therefore its y-intercept is $-4$. This means that the tentative equation of the given line is $y=mx - 4$ The line contains the point $(-3, 0)$, to the coordinates of this point satisfy the equation of the line. Substitute the x and y coordinates of this point into the tentative equation of the line to have: $y=mx-4 \\0=m(-3)-4 \\0=-3m-4 \\3m=-4 \\m=-\frac{4}{3}$ Therefore, the equation of the line is $y=-\frac{4}{3}x-4$.
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