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:
$\begin{align}
& m=\frac{42-26}{180-80} \\
& =\frac{16}{100} \\
& =0.16
\end{align}$
Thus, the slope of the line is\[0.16\].
(b)
The slope of the line shows the change in the percentage of the patients with depression in remission for each minute of brisk walking. The value of the slope is positive. This shows that the percentage increases and is equal to 0.16%. This percentage increase represents the rate of change. The rate of change is 0.16% per minute.
Thus, for each minute of brisk walking, the percentageof the patients with depression in remissionincreased by 0.16%. The rate of change is 0.16% per minute.
Hence, the percentage increase is 0.16% and the rate of change is 0.16% per minute as the value of the slope is positive.
