Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.4 - Linear Functions and Slope - Exercise Set - Page 152: 42

Answer

$a.\qquad y=-3x$ $b.\qquad\left\{\begin{array}{ll} m=-3, & \text{slope}\\ b=0 & \text{y-intercept} \end{array}\right.$ $c. \qquad $Graph:
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Work Step by Step

$(a)$ The slope-intercept form is $\ \ y=mx+b.$ ( m= slope, b= y-intercept) Solve for y: $\left[\begin{array}{l} 2x+y=0\\ y=-3x\\ \end{array}\right]$ $(b)$ $y=-3x+0\ \Rightarrow \ \left\{\begin{array}{ll} m=-3, & \text{slope}\\ b=0 & \text{y-intercept} \end{array}\right.$ $(c)$ Graphing, we have a starting point,$ (0,0)$, since b=0. Now, the slope $m=\displaystyle \frac{\text{change in y}}{\text{change in x}}=-3=\frac{-3}{1} $, which we use like this: Increasing x by 1 (from x=0 to x=1), y decreases by $3$ units (from y=0 to y=$-3$). The line passes through $(1,-3).$ Two points define the line. Draw it.
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