# How do you write the equation of the line that has contains the point (5, -4) and has a slope of 5?

Jan 10, 2017

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

or

$y = \textcolor{b l u e}{5} x - 29$

#### Explanation:

We can use the point-slope formula to determine the equation of the line in this problem.

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 point from the problem gives:

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

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

We can put this in the more familiar slope-intercept form by solving for $y$:

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

$y + \textcolor{red}{4} = \textcolor{b l u e}{5} x - 25$

$y + \textcolor{red}{4} - 4 = \textcolor{b l u e}{5} x - 25 - 4$

$y + 0 = \textcolor{b l u e}{5} x - 29$

$y = \textcolor{b l u e}{5} x - 29$