## Intermediate Algebra (6th Edition)

$\frac{2}{3}$
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. $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $m=\frac{4-0}{0-(-6)}=\frac{4}{6}=\frac{2}{3}$