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: 27

Answer

$y=\dfrac{2}{3}x+\dfrac{19}{3}$

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 $m=\frac{2}{3}$ and passes through the point $(1, 7)$. Thus, the tentative equation of the line is: $y=\dfrac{2}{3}(x)+b$ To find the value of $b$, substitute the coordinates of $(1, 7)$ into the tentative equation above to obtain: $y=\dfrac{2}{3}x+b \\7 = \dfrac{2}{3}(1) + b \\7 = \dfrac{2}{3} + b \\7-\dfrac{2}{3} = b \\\dfrac{21}{3} - \dfrac{2}{3}=b \\\dfrac{19}{3} = b$ Therefore, the equation of the line is: $y=\dfrac{2}{3}x+\dfrac{19}{3}$
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