# How do you write an equation in standard form for a line passing through(–2, 1) and (4, 13)?

May 11, 2015

The equation is : $y = 2 x + 5$

Any linear function has the following form : $y = m x + b$

Firstly, you need to find the slope $m$ of your line.

It is given by :

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

where $\left({x}_{1} , {y}_{1}\right) = \left(- 2 , 1\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(4 , 13\right)$ or vice versa.

So $m = \frac{13 - 1}{4 + 2} = 2$.

Then, in order to find $b$, you have to solve the following equation :

${y}_{1} = m {x}_{1} + b$ or
${y}_{2} = m {x}_{2} + b$

So $1 = 2 \cdot \left(- 2\right) + b \implies b = 5$

Now you have the equation of your line :

$y = 2 x + 5$