What is the slope of the line passing through the following points: (3,2),(1,-3) ?

Slope is $\frac{5}{2}$
Slope of a line passing through two points is given by $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.
Hence in the instant case, slope between the two points is given by $\frac{- 3 - 2}{1 - 3}$ or $\frac{- 5}{-} 2$
or $\frac{5}{2}$