Answer
(a) $-\dfrac{1}{3}$
(b) For every $3$-unit increase in $x$, there corresponds a $1$ unit decrease in $y$.
Work Step by Step
(a) The slope $m$ of the line through the points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula:
$m=\dfrac{y_2-y_1}{x_2-x_1}$
Plug the $x$ and $y$ values of the given points into the formula to obtain:
$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-1}{-2-1}=-\dfrac{1}{3}$
(b) The slope is the change in $y$ divided by the change in $x$ and is also known as "rise over run."
Thus, having a slope of $-\frac{1}{3}$ means that for every unit increase in the value of $x$, there corresponds a decrease of $\frac{1}{3}$ of a unit in the value of $y$.
This is equivalent to saying that for every $3$-unit increase in the value of $x$, there corresponds a decrease of $1$ unit in the value of $y$.
