# How do you write the equation in slope intercept form given (–5, 8), (–4, –6)?

Jan 4, 2017

$y = - 14 x - 62$

#### Explanation:

When given two points we can use the point-slope formula to obtain the equation for the line and then convert to the slope-intercept form.

To use the point-slope formula we must first calculate the slope using the two points.

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 two points from the problem gives:

$m = \frac{\textcolor{red}{- 6} - \textcolor{b l u e}{8}}{\textcolor{red}{- 4} - \textcolor{b l u e}{- 5}}$

$m = \frac{\textcolor{red}{- 6} - \textcolor{b l u e}{8}}{\textcolor{red}{- 4} + \textcolor{b l u e}{5}}$

$m = \frac{- 14}{1}$

$m = - 14$

Now, having obtained the slope we can use the point-slope formula using the slope we have calculated and either of the points.

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.

Substituting the slope and one of the points gives:

$\left(y - \textcolor{red}{- 6}\right) = \textcolor{b l u e}{- 14} \left(x - \textcolor{red}{- 4}\right)$

$\left(y + \textcolor{red}{6}\right) = \textcolor{b l u e}{- 14} \left(x + \textcolor{red}{4}\right)$

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

$y + \textcolor{red}{6} = \textcolor{b l u e}{- 14} x + \left(\textcolor{b l u e}{- 14} \times \textcolor{red}{4}\right)$

$y + \textcolor{red}{6} = \textcolor{b l u e}{- 14} x - 56$

$y + \textcolor{red}{6} - 6 = \textcolor{b l u e}{- 14} x - 56 - 6$

$y + 0 = \textcolor{b l u e}{- 14} x - 62$

$y = \textcolor{b l u e}{- 14} x - 62$