Answer
(a) Slope $= -3$ and y-intercept $=4$
(b) See the image.
(c) Average rate of change $= -3$
(d) The linear function $h(x)=-3x+4$ is decreasing.
Work Step by Step
Step-1: Compare the given equation with the point-slope 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 $$h(x)=-3x+4$$ to $$h(x) = mx+b$$ we that understand that the slope of the given function is $-3$ 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 $x=-2$, $h(x)=10$
For $x=-1$, $h(x)=7$
For $x=0$, $h(x)=4$
For $x=1$, $h(x)=1$
For $x=2$, $h(x) = -2$
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 $x_1=-2$,
$$\frac{\Delta y}{\Delta x}=\frac{-2-10}{2-(-2)}=-3$$
Step-4: Since slope, $m=-3<0$, this linear function is decreasing.
