# How do you find a standard form equation for the line with (-6, 0) and (2, -9)?

Aug 24, 2016

$y = - \frac{9}{8} x - \frac{27}{4}$

#### 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.

We have to find the values of m and b.

To calculate 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 $\left({x}_{1} , {y}_{1}\right) \text{ are 2 coordinate points}$

here the 2 points are (-6 ,0) and (2 ,-9)

let $\left({x}_{1} , {y}_{1}\right) = \left(- 6 , 0\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(2 , - 9\right)$

$\Rightarrow m = \frac{- 9 - 0}{2 + 6} = \frac{- 9}{8} = - \frac{9}{8}$

We can now write a partial equation as $y = - \frac{9}{8} x + b$

To calculate b, use either of the 2 given points that lie on the line.

Using (2 ,-9)That is x= 2 and y = -9 , substitute in partial equation

$\Rightarrow \left(- \frac{9}{8} \times 2\right) + b = - 9 \Rightarrow - \frac{9}{4} + b = - 9 \Rightarrow b = - \frac{27}{4}$

$\Rightarrow y = - \frac{9}{8} x - \frac{27}{4} \text{ is the equation of the line}$