# How do you find the slope of every line parallel to the points (4, 3) and (2,-5)?

Mar 15, 2017

See the entire solution process below

#### Explanation:

By definition, two parallel lines have the same slope. Therefore, if we determine the slope of the line going through these two points we have found the slope of every line parallel to this 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:

$m = \frac{\textcolor{red}{- 5} - \textcolor{b l u e}{3}}{\textcolor{red}{2} - \textcolor{b l u e}{4}} = \frac{- 8}{-} 2 = 4$