# How do you find the slope of the line passing through the points A(4, 2) and B(-2, 4)?

Mar 9, 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)

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

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

$m = - \frac{1}{3}$

#### Explanation:

Given:
$A \equiv \left(4 , 2\right)$
$B \equiv \left(- 2 , 4\right)$
Slope of the line connecting the two points
$A \equiv \left({x}_{1} , {y}_{1}\right) \text{ and "B-=(x_2,y_2)" is given by}$
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
Here, we have
${x}_{1} = 4$
${y}_{1} = 2$
${x}_{2} = - 2$
${y}_{2} = 4$
${y}_{2} - {y}_{1} = 4 - 2$
${y}_{2} - {y}_{1} = 2$
${x}_{2} - {x}_{1} = - 2 - 4$
${x}_{2} - {x}_{1} = - 6$
Now,
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{2}{-} 6$
$m = - \frac{1}{3}$