# What is the equation in point-slope form of the line given (5,7),(6,8)?

May 26, 2015

The slope of a line given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given points $\left(5 , 7\right)$ and $\left(6 , 8\right)$
$m = \frac{8 - 7}{6 - 5} = 1$

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

For our given values this is
$\left(y - 7\right) = \left(1\right) \left(x - 5\right)$