# How do you find the slope given (9,3) and (4,2)?

May 15, 2018

See a solution process below:

#### Explanation:

The formula for find the slope of a line is:

$m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ and $\left(\textcolor{red}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right)$ are two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{2} - \textcolor{b l u e}{3}}{\textcolor{red}{4} - \textcolor{b l u e}{9}} = \frac{- 1}{-} 5 = \frac{1}{5}$

May 15, 2018

$m$ = $\frac{1}{5}$

#### Explanation:

When given two points, use this equation to find the slope:

$\frac{{Y}_{2} - {Y}_{1}}{{X}_{2} - {X}_{1}}$ = $m$, the slope

Your ordered pairs will be labeled as the $y$'s and $x$'s in order to plug it into this equation. Let's label them:

$\left(9 , 3\right)$ $\left({X}_{1} , {Y}_{1}\right)$
$\left(4 , 2\right)$ $\left({X}_{2} , {Y}_{2}\right)$

Now, plug your variables into the equation. Use what you've labeled as a reference.

$\frac{2 - 3}{4 - 9}$ = $m$

Subtract and simplify.

$\frac{- 1}{- 5}$ = $m$

Because two negatives create a positive, the slope becomes $\frac{1}{5}$.
Therefore, $m$ = $\frac{1}{5}$.