Calculate the slope (m).

The formula for the slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Using the points $(x_1, y_1) = (2, 4)$ and $(x_2, y_2) = (5, 13)$:

$$m = \frac{13 - 4}{5 - 2}$$ $$m = \frac{9}{3}$$ $$m = 3$$

Substitute the slope $m=3$ and one of the points (e.g., $(2, 4)$) into the equation $y = mx + c$:

$$4 = (3)(2) + c$$ $$4 = 6 + c$$ $$c = 4 - 6$$ $$c = -2$$

Substitute the values of $m$ and $c$ into $y = mx + c$:

$$y = 3x - 2$$