Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 18: 4


Slope: $m=\dfrac{1}{2}$ $x$-intercept $=$ $y$-intercept $=$ $(0,0)$

Work Step by Step

$y-3=\dfrac{1}{2}(x-6)$ Express this equation in slope-intercept form by solving it for $y$: $y-3=\dfrac{1}{2}x-\dfrac{6}{2}$ $y-3=\dfrac{1}{2}x-3$ $y=\dfrac{1}{2}x-3+3$ $y=\dfrac{1}{2}x$ This line is now in slope-intercept form, which is $y=-mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept. Comparing the given line to the slope-intercept form, it can be seen that $m=\dfrac{1}{2}$ and $b=0$ The slope of the given line is $m=\dfrac{1}{2}$ and its $y$-intercept is the origin, $(0,0)$ Since the $y$-intercept is the origin, then the $x$-intercept of this line is also the point $(0,0)$
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