# What is the equation of the line between (5,13) and (-1,3)?

Dec 7, 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:
$m = \frac{3 - 13}{- 1 - 5} = \frac{5}{3}$

$y - 13 = \left(\frac{5}{3}\right) x - 5$

$5 x - 3 y + 14 = 0$