# How do you write the slope intercept form of the equation of through (-5,-5) and (1,-3)?

Jan 4, 2017

See full solution process below:

#### Explanation:

Because we are given two points on the line we will use the point-slope formula to solve this problem. However, we first need to determine the slope, then we can use either point to determine the equation.

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 we were given into the formula gives:

$m = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{- 5}}{\textcolor{red}{1} - \textcolor{b l u e}{- 5}}$

$m = \frac{2}{6} = \frac{1}{3}$

Now that we have the slope we can use it and one of the points with the point-slope formula to find the equation for the line.

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 we calculate and one of the points into this formula gives:

$\left(y - \textcolor{red}{- 5}\right) = \textcolor{b l u e}{\frac{1}{3}} \left(x - \textcolor{red}{- 5}\right)$

$\left(y + \textcolor{red}{5}\right) = \textcolor{b l u e}{\frac{1}{3}} \left(x + \textcolor{red}{5}\right)$

We can convert to the more familiar slope-intercept form of the equation for this line by solving for $y$ as follows:

$y + \textcolor{red}{5} = \textcolor{b l u e}{\frac{1}{3}} x + \left(\textcolor{b l u e}{\frac{1}{3}} \times \textcolor{red}{5}\right)$

$y + \textcolor{red}{5} = \textcolor{b l u e}{\frac{1}{3}} x + \frac{5}{3}$

$y + \textcolor{red}{5} - 5 = \textcolor{b l u e}{\frac{1}{3}} x + \frac{5}{3} - 5$

$y + 0 = \textcolor{b l u e}{\frac{1}{3}} x + \frac{5}{3} - \frac{15}{3}$

$y = \textcolor{b l u e}{\frac{1}{3}} x - \frac{10}{3}$