# How do you write an equation in point slope form that passes through ( -1,0) , (3, 10)?

Jun 2, 2015

Slope is (change in $y$) / (change in $x$)...

More formally: Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ the slope $m$ of a straight line passing through those points is given by the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

In your example, with $\left({x}_{1} , {y}_{1}\right) = \left(- 1 , 0\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(3 , 10\right)$,

$m = \frac{10 - 0}{3 - \left(- 1\right)} = \frac{10}{4} = \frac{5}{2}$

Point-slope form looks like:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$, where $m$ is the slope and $\left({x}_{0} , {y}_{0}\right)$ is a point through which the line passes.

I will use the point $\left(3 , 10\right)$ to write the equation of our line as:

$y - 10 = \frac{5}{2} \left(x - 3\right)$