# How do you write the equation in slope intercept form given (-2,-8) and (2,-6)?

Jul 4, 2016

$y = \frac{1}{2} x - 9$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

m and b have to be found to complete the equation of the line.

To find m use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

Here the 2 points are (-2 ,-8) and (2 ,-6)

let $\left({x}_{1} , {y}_{1}\right) = \left(- 2 , - 8\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(2 , - 6\right)$

$\Rightarrow m = \frac{- 6 - \left(- 8\right)}{2 - \left(- 2\right)} = \frac{2}{4} = \frac{1}{2}$

The same result is obtained if the coordinate points are reversed.

The partial equation is $y = \frac{1}{2} x + b$

To find b, use either of the 2 given points and substitute in the partial equation.
Using (2 ,-8) with x = 2 and y = -8

$\left(\frac{1}{2} \times 2\right) + b = - 8 \Rightarrow 1 + b = - 8 \Rightarrow b = - 9$

$\Rightarrow y = \frac{1}{2} x - 9 \text{ is the equation}$