# How do you write an equation of a line with point (-1,4), slope -1?

Jan 22, 2017

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x + \textcolor{red}{1}\right)$

Or

$y = - x + 3$

#### Explanation:

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 values from the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{- 1}\right)$

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x + \textcolor{red}{1}\right)$

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

$y - \textcolor{red}{4} = \left(\textcolor{b l u e}{- 1} \times x\right) + \left(\textcolor{b l u e}{- 1} \times \textcolor{red}{1}\right)$

$y - \textcolor{red}{4} = - 1 x - 1$

$y - \textcolor{red}{4} + 4 = - x - 1 + 4$

$y - 0 = - x + 3$

$y = - x + 3$