Question

Find the equation in standard form of the line passing through the points (2,-3) and (4,2)

Answer 1

The equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$\frac{x-x_1}{y-y_1} =\frac{x_2-x_1}{y_2-y_1}$. Here $\frac{y_1-y_1}{x_2-x_1}$ is the slope of the line.

Substituting numerical values,

$\frac{x-2}{y+3} =\frac{4-2}{2+3} \\ \frac{x-2}{y+3} =\frac{2}{5} \\ 5x-10=2y+6\\ 5x-2y-16=0$

The equation of the line in standard form is $5x-2y-16=0$.