# How do you write an equation in slope intercept form given (-3, -1) and (-6, 8)?

Jan 29, 2017

$y = - 3 x - 10$

#### Explanation:

First we must determine the slope. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the equation gives:

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{- 1}}{\textcolor{red}{- 6} - \textcolor{b l u e}{- 3}}$

$m = \frac{\textcolor{red}{8} + \textcolor{b l u e}{1}}{\textcolor{red}{- 6} + \textcolor{b l u e}{3}}$

$m = \frac{9}{-} 3 = - 3$

We can now use the calculated slope and the first point to write an equation in the point-slope form. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through. Substitution gives:

$\left(y - \textcolor{red}{- 1}\right) = \textcolor{b l u e}{- 3} \left(x - \textcolor{red}{- 3}\right)$

$\left(y + \textcolor{red}{1}\right) = \textcolor{b l u e}{- 3} \left(x + \textcolor{red}{3}\right)$

We can now solve for $y$ to put the equation in slope intercept form.

$y + \textcolor{red}{1} = \left(\textcolor{b l u e}{- 3} \times x\right) + \left(\textcolor{b l u e}{- 3} \times \textcolor{red}{3}\right)$

$y + \textcolor{red}{1} = - 3 x - 9$

$y + \textcolor{red}{1} - 1 = - 3 x - 9 - 1$

$y = - 3 x - 10$