Two coordinates of the graph of function p is,
(x1, y1)=(0,-7)
(x2,y2)=(-6,-3)
Now, the slope of the graph is,
[tex]\begin{gathered} \frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-3-(-7)}{-6-0} \\ =\frac{-3+7}{-6} \\ =\frac{4}{-6} \\ =\frac{-2}{3} \end{gathered}[/tex]
Consider two points of the function h(x).
(x1,y1)=(0,-6).
(x2,y2)=(3,-8).
The slope of graph of function h(x) is,
[tex]\begin{gathered} \text{Slope=}\frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-8-(-6)}{3-0} \\ =\frac{-8+6}{3} \\ =\frac{-2}{3} \end{gathered}[/tex]
The slopes of the graphs of functions gives the rate of change of the function.
Since the slopes of graphs of both functions h(x) and p(x) is -2/3, the functions decrease at a constant rate.
Therefore, option C is correct.
