## College Algebra (10th Edition)

(a) Slope $= -1$ and y-intercept $=6$ (b) See the image. (c) Average rate of change $= 6$ (d) The linear function $p(x)=-x+6$ is decreasing.
Step-1: Compare the given equation with the slope-intercept form of the linear equation, that is, $p(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$p(x)=-x+6$$ to $$p(x) = mx+b$$ we that understand that the slope of the given function is $-1$ and its y-intercept is $6$. 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 $x=-2$, $f(x)=8$ For $x=-1$, $f(x)=7$ For $x=0$, $f(x)=6$ For $x=1$, $f(x)=5$ For $x=2$, $f(x) = 4$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{\Delta y}{\Delta x}=\frac{p(x_2)-p(x_1)}{x_2-x_1}$$ Let us calculate average rate of change between $x_2=2$ and $x_1=-2$, $$\frac{\Delta y}{\Delta x}=\frac{4-8}{2-(-2)}=-1$$ Step-4: Since slope, $m=-1<0$, this linear function is decreasing.