# What is the equation of a line that goes through the points (-12, 3) and (8, 15)?

Dec 3, 2015

the equation of a line passing through 2 points $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right)$ is given as:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$\mathmr{and} m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ called the slope of the line

therefore putting the given points in the above equation we end up getting:

$m = \frac{15 - 3}{8 - \left(- 12\right)} = \frac{12}{20} = \frac{3}{5}$

$y - 3 = \left(\frac{3}{5}\right) \left(x - \left(- 12\right)\right)$
$5 y - 15 = 3 x + 36$
$3 x - 5 y + 51 = 0$