Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 3 - Cumulative Review: 45

Answer

$\frac{2}{3}$

Work Step by Step

We are given that $f(x)=\frac{2}{3}x+4$. Two points are needed to calculate the slope of a line. We can calculate the value of its intercepts to find two points. If $x=0$, $f(0)=\frac{2}{3}\times0+4=4$. If $y=0$, $0=\frac{2}{3}x+4$. Subtract 4 from both sides. $-4=\frac{2}{3}x$. Multiply both sides by $\frac{3}{2}$. $x=-6$ Therefore, (-6,0) and (0,4) are both points on this line. We can use the slope formula to calculate the line. $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $m=\frac{4-0}{0-(-6)}=\frac{4}{6}=\frac{2}{3}$
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