Standard Form
You can convert directly two points on a line into a standard form equation using the formula
\[ a = y_2 - y_1 \]
\[ b = x_1 - x_2 \]
\[ c = a \cdot x_1 + b \cdot x_2 \]
This will not usually produce the simplest formula for the equation. It works well for computer code if you just need to work with a linear system of coefficients.