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: 34



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 slope of a line can be found using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. The x-intercept is $-8$ so the point $(-8, 0)$ is on the line. The y-intercept is $6$, so $b=6$. Thus, the tentative equation of the line is: $y=mx+6$ To find the value of $b$, substitute the x and y coordinates of the point $(-8, 0)$ into the tentative equation above to obtain: $y=mx+6 \\0=m(-8)+6 \\0=-8m+6 \\0+8m=6 \\8m=6 \\\dfrac{8m}{8}=\dfrac{6}{8} \\m=\dfrac{3}{4}$ Therefore, the equation of the line is: $y=\dfrac{3}{4}x+6$
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