# How do you find the point-slope form of the equation of the line passing through the points (15, 16), (13, 10)?

May 27, 2015

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
the slope is given by the formula
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$

Given the points $\left(15 , 16\right)$ and $\left(13 , 10\right)$
the slope is $m = \frac{16 - 10}{15 - 13} = \frac{6}{2} = 3$

Given a slope $m$ and a point $\left({x}_{1} , {y}_{1}\right)$
the point-slope form of the linear equation is
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

For the given values this becomes
$y - 16 = 3 \left(x - 15\right)$