Answer
a) Slope: $\dfrac{4}{5}x$;
b) $y$-intercept: -6;
c) see graph
d) $h$ is increasing
Work Step by Step
We are given the function:
$h(x)=\dfrac{4}{5}x-6$
a) Determine the slope of the function, using the standard form $y=mx+b$:
$m=\dfrac{4}{5}$
Determine the $y$-intercept:
$b=-6$
b) Determine the average rate of change:
$\dfrac{\Delta y}{\Delta x}=m=\dfrac{4}{5}$
c) Determine the $x$-intercepts:
$y=0\Rightarrow \dfrac{4}{5}x-6=0\Rightarrow x=\dfrac{15}{2}$
Graph the function using the intercepts:
d) As the slope is positive, the function is increasing on $(-\infty,\infty)$.
