# How do you write an equation that contains points (4, -1) and (-2, -13)?

Apr 20, 2018

$y = 2 x - 9$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(4,-1)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , - 13\right)$

$\Rightarrow m = \frac{- 13 - \left(- 1\right)}{- 2 - 4} = \frac{- 12}{- 6} = 2$

$\Rightarrow y = 2 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(4,-1)" then}$

$- 1 = 8 + b \Rightarrow b = - 1 - 8 = - 9$

$\Rightarrow y = 2 x - 9 \leftarrow \textcolor{red}{\text{is equation of line}}$