What is the slope of the line passing through the following points:  (4, 2) , (-2, 4)?

Mar 30, 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:

$m = \frac{\textcolor{red}{4} - \textcolor{b l u e}{2}}{\textcolor{red}{- 2} - \textcolor{b l u e}{4}} = \frac{2}{-} 6 = - \frac{1}{3}$

Mar 30, 2018

$\text{slope } = - \frac{1}{3}$

Explanation:

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(4,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 4\right)$

$\Rightarrow m = \frac{4 - 2}{- 2 - 4} = \frac{2}{- 6} = - \frac{1}{3}$