# How do you write an equation in slope intercept form of the line that passes through (4, 1) and (5, -1)?

Mar 17, 2017

See the entire solution process below:

#### 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:

$m = \frac{\textcolor{red}{- 1} - \textcolor{b l u e}{1}}{\textcolor{red}{5} - \textcolor{b l u e}{4}} = - \frac{2}{1} = - 2$

Next, we can use the point slope formula to write 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 we calculated and the first point from the problem gives:

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{- 2} \left(x - \textcolor{red}{4}\right)$

We can now 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.

$y - \textcolor{red}{1} = \left(\textcolor{b l u e}{- 2} \times x\right) - \left(\textcolor{b l u e}{- 2} \times \textcolor{red}{4}\right)$

$y - \textcolor{red}{1} = - 2 x - \left(- 8\right)$

$y - \textcolor{red}{1} = - 2 x + 8$

$y - \textcolor{red}{1} + 1 = - 2 x + 8 + 1$

$y - 0 = - 2 x + 9$

$y = \textcolor{red}{- 2} x + \textcolor{b l u e}{9}$