Answer
See below:
Work Step by Step
(a)
Consider the information provided and study the graph carefully.
Recall the formula to calculate the slope of the equation of line:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substitute the values in the above equation to find slope:
$\begin{align}
& m=\frac{29-49}{62-22} \\
& =\frac{-20}{40} \\
& =-0.5
\end{align}$
The slope of the line obtained above is negative. This shows that the percentage of people reporting a lot of stress decreases with age.
Thus, the slope of the line is $-0.5$.
(b)
The slope of the line shows the change in the percentage of the Americans reporting “a lot” of stress for each year of aging. The value of the slope is negative. This shows that the percentage decreases and is equal to 0.5%. This decrease represents the rate of change. So, the rate of change is 0.5% per year of aging.
Thus, the percentage of Americans reporting “a lot” of stress decreases by 0.5% and the rate of change is 0.5% per year of aging.
For each year of aging, the percentage of Americans reporting “a lot” of stress decreases by \[0.5%\]. The rate of change is \[0.5%\] per year of aging.
