College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises - Page 113: 28



Work Step by Step

RECALL: The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept. The given line has $m=-\frac{7}{2}$ and passes through the point $(-3, -5)$. Thus, the tentative equation of the line is: $y=-\dfrac{7}{2}(x)+b$ To find the value of $b$, substitute the coordinates of $(-3, -5)$ into the tentative equation above to obtain: $y=-\dfrac{7}{2}x+b \\-5 = -\dfrac{7}{2}(-3) + b \\-5 = \dfrac{21}{2} + b \\-5-\dfrac{21}{2} = b \\-\dfrac{10}{2} - \dfrac{21}{2}=b \\-\dfrac{31}{2} = b$ Therefore, the equation of the line is: $y=-\dfrac{7}{2}x-\dfrac{31}{2}$
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