# What is the slope of the line passing through the following points: (5,3) , (–3, 5) ?

##### 2 Answers
Mar 12, 2018

See a solution process below:

#### Explanation:

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:

$m = \frac{\textcolor{red}{5} - \textcolor{b l u e}{3}}{\textcolor{red}{- 3} - \textcolor{b l u e}{5}} = \frac{2}{-} 8 = - \frac{1}{4}$

Mar 12, 2018

$\text{slope } = - \frac{1}{4}$

#### Explanation:

$\text{calculate the slope m using the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(5,3)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 3 , 5\right)$

$\Rightarrow m = \frac{5 - 3}{- 3 - 5} = \frac{2}{- 8} = - \frac{1}{4}$