# How do you write the equation in slope intercept form given (5,7) (1,-9)?

Feb 1, 2017

$y = 4 x - 13$

#### Explanation:

First, we need to 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 problem gives:

$m = \frac{\textcolor{red}{- 9} - \textcolor{b l u e}{7}}{\textcolor{red}{1} - \textcolor{b l u e}{5}}$

$m = \frac{- 16}{-} 4 = 4$

We can now use the point-slope formula to find an 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 and the first point in the problem gives:

$\left(y - \textcolor{red}{7}\right) = \textcolor{b l u e}{4} \left(x - \textcolor{red}{5}\right)$

Now, solve for $y$ to put the equation in slope intercept form:

$y - \textcolor{red}{7} = \left(\textcolor{b l u e}{4} \times x\right) - \left(\textcolor{b l u e}{4} \times \textcolor{red}{5}\right)$

$y - \textcolor{red}{7} = 4 x - 20$

$y - \textcolor{red}{7} + 7 = 4 x - 20 + 7$

$y - 0 = 4 x - 13$

$y = 4 x - 13$