What is the slope of the line passing through the following points:  (-1/3, 3/5), (-3/4, 5/3)?

When you have two points lets say $A \left({x}_{A} , {y}_{A}\right)$ and $B \left({x}_{B} , {y}_{B}\right)$ the equation of the line that passes through these points is
$y - {y}_{B} = k \cdot \left(x - {x}_{B}\right)$
where $k = \frac{{y}_{B} - {y}_{A}}{{x}_{B} - {x}_{A}}$ is the slope of the line.
$k = \frac{\frac{5}{3} - \frac{3}{5}}{- \frac{3}{4} + \frac{1}{3}} = \frac{\frac{16}{15}}{- \frac{5}{12}} = - \frac{64}{25}$