# How do you write an equation of a line given point (-4,-2) and (4,0)?

##### 1 Answer
Apr 19, 2017

See the entire solution process below:

#### Explanation:

First, we need to determine the slope of the line. 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:

$m = \frac{\textcolor{red}{0} - \textcolor{b l u e}{- 2}}{\textcolor{red}{4} - \textcolor{b l u e}{- 4}} = \frac{\textcolor{red}{0} + \textcolor{b l u e}{2}}{\textcolor{red}{4} + \textcolor{b l u e}{4}} = \frac{2}{8} = \frac{1}{4}$

We can 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 we calculated and the values from the first point in the problem gives:

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

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

We can also substitute the slope we calculated and the values from the second point in the problem giving:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{1}{4}} \left(x - \textcolor{red}{4}\right)$

We can solve this for equation 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.

$y - \textcolor{red}{0} = \left(\textcolor{b l u e}{\frac{1}{4}} \times x\right) - \left(\textcolor{b l u e}{\frac{1}{4}} \times \textcolor{red}{4}\right)$

$y = \frac{1}{4} x - \frac{\textcolor{red}{4}}{\textcolor{b l u e}{4}}$

$y = \textcolor{red}{\frac{1}{4}} x - \textcolor{b l u e}{1}$