# What is the slope of the line passing through the following points:  (3/5,2) ; (2/10,5/4) ?

$m = \frac{15}{8}$
To find the slope given two points, we use the gradient formula: $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, where ${x}_{1} , {y}_{1}$ are the coordinates of the the first point and ${x}_{2} , {y}_{2}$ are the coordinates of the second point and $m$ is the slope (and its what we're trying to find). Lets call $\left(\frac{3}{5} , 2\right)$ the first point, and $\left(\frac{2}{10} , \frac{5}{4}\right)$ the second point. It doesn't matter which one we call the first or second point, the answer will always be the same Applying the formula, we get the answer:
$m = \frac{\frac{5}{4} - 2}{\frac{2}{10} - \frac{3}{5}}$
$m = \frac{\frac{5}{4} - \frac{8}{4}}{\frac{1}{5} - \frac{3}{5}}$
$m = \frac{- \frac{3}{4}}{- \frac{2}{5}}$
$m = \frac{15}{8}$