Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 1 - Linear Functions - 1.1 Slopes and Equations of Lines - 1.1 Exercises - Page 13: 25



Work Step by Step

$x$-intercept: $-6$ $,$ $y$-intercept: $-3$ The line's intercepts are given. These represent the points $(-6,0)$ and $(0,-3)$. Find the slope of the line substituting its intercepts into the formula $m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$: $m=\dfrac{-3-0}{0-(-6)}=\dfrac{-3}{6}=-\dfrac{1}{2}$ The point-slope form of the equation of a line is $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept. Both the slope of the line and its $y$-intercept are known. Substitute them into the formula and simplify: $y=-\dfrac{1}{2}x-3$ Multiply the whole equation by $2$: $2\Big(y=-\dfrac{1}{2}x-3\Big)$ $2y=-x-6$ Take all terms to the left side: $x+2y+6=0$
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