# How do you write an equation of a line with point (1,5) slope -1?

Jun 27, 2017

See a solution process below:

#### 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 $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

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

We can solve for $y$ to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

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

$y - \textcolor{red}{5} = - 1 x - \left(- 1\right)$

$y - \textcolor{red}{5} = - 1 x + 1$

$y - \textcolor{red}{5} + 5 = - 1 x + 1 + 5$

$y - 0 = - 1 x + 6$

$y = \textcolor{red}{- 1} x + \textcolor{b l u e}{6}$