Answer
The slope of the line passing through the points $\left( 3,2 \right)$ and $\left( 5,1 \right)$ is $-\frac{1}{2}$ and this line falls.
Work Step by Step
The slope of the line passing through two points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is provided by the formula $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$.
Now, compute the slope of the line passing through the points $\left( 3,2 \right)$ and $\left( 5,1 \right)$ as shown below:
$\begin{align}
& m=\frac{1-2}{5-3} \\
& =-\frac{1}{2}
\end{align}$
Therefore, the slope of this line is $-\frac{1}{2}$.
Now, as the slope of the line is negative, hence the line falls.
Therefore, the slope of the line passing through the points $\left( 3,2 \right)$ and $\left( 5,1 \right)$ is $-\frac{1}{2}$ and this line falls.
