# How do you write the equation of the line passing through the points (-2,3) and (-4,1)?

Apr 24, 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:

$m = \frac{\textcolor{red}{1} - \textcolor{b l u e}{3}}{\textcolor{red}{- 4} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{1} - \textcolor{b l u e}{3}}{\textcolor{red}{- 4} + \textcolor{b l u e}{2}} = \frac{- 2}{-} 2 = 1$

Now, 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:

$\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{1} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{1} \left(x + \textcolor{red}{2}\right)$

We can now solve for $y$ to put the equation in slope-intercept form:

$y - \textcolor{red}{3} = x + 2$

$y - \textcolor{red}{3} + 3 = x + 2 + 3$

$y = x + 5$