Answer
See below:
Work Step by Step
(a)
By the definition of slope:
\[m=\left( \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)\]
The given points are:
\[\left( 1985,64 \right)\], and\[\left( 2010,52 \right)\].
So,
\[\begin{align}
& m=\left( \frac{52-64}{2010-1985} \right) \\
& =-0.48
\end{align}\]
Therefore, the slope of the line is\[-0.48\].
(b)
The line passing through the two points\[\left( 1985,64 \right)\], and\[\left( 2010,52 \right)\].
The change of emotional health (in percentage) will be:
={52-64}/{2010-1985}%
={-12}/{25} %
=-0.48%
Therefore, the percentage of U. S college freshman rating their emotional health high or above average decreased by\[0.48%\]. The rate of change was \[-0.48%\]per year.
