# How do you find an equation of the line that passes through (3,-1) and (-2,9) and write the equation using function notation?

Jun 7, 2015

If a point passes through points $\left(3 , - 1\right)$ and $\left(- 2 , 9\right)$
its slope is $m = \frac{\Delta y}{\Delta x} = \frac{9 - \left(- 1\right)}{\left(- 2\right) - 3} = - 2$

The general form of a line passing through $\left(3 , - 1\right)$ with as slope of $\left(- 2\right)$ is
$\textcolor{w h i t e}{\text{XXXX}}$$y - \left(- 1\right) = \left(- 2\right) \left(x - 3\right)$
which simplifies as
$\textcolor{w h i t e}{\text{XXXX}}$$y = 5 - 2 x$

in function notation:
$\textcolor{w h i t e}{\text{XXXX}}$$f \left(x\right) = 5 - 2 x$