## College Algebra (10th Edition)

(a) Slope $= -\frac{2}{3}$ and y-intercept $=4$ (b) See the image. (c) Average rate of change $=-\frac{2}{3}$ (d) The linear function $h(x)=-\frac{2}{3}x+4$ is decreasing.
Step-1: Compare the given equation with the slope-intercept form of the linear equation, that is, $h(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$h(x)=-\frac{2}{3}x+4$$ to $$h(x) = mx+b$$ we understand that the slope of the given function is $-\frac{2}{3}$ and its y-intercept is $4$. Step-2: Let us put values of $x$ from $-2$ to $2$ into the function to obtain corresponding $y$ values. Using this we can plot a graph. Thus, For $x=-2$, $h(x)=\frac{16}{3}=5.33$ For $x=-1$, $h(x)=\frac{14}{3}=4.67$ For $x=0$, $h(x)=4$ For $x=1$, $h(x)=\frac{10}{3}=3.33$ For $x=2$, $h(x) = \frac{8}{3}=2.67$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{\Delta y}{\Delta x}=\frac{h(x_2)-h(x_1)}{x_2-x_1}$$ Let us calculate average rate of change between $x_2=2$ and $x_1=-2$, $$\frac{\Delta y}{\Delta x}=\frac{\frac{8}{3}-\frac{16}{3}}{2-(-2)}=-\frac{2}{3}=-0.67$$ Step-4: Since slope, $m=-0.67<0$, this linear function is decreasing.