# How do you find the slope of a line given the points (2,2) and (5,8) on the line?

May 24, 2017

$m = \frac{6}{3} = 2$

#### Explanation:

Slope means the steepness or gradient of a line.

It can be described as the " "("change in the y-values")/("change in the x-values")

which is sometimes explained as $\left(\text{rise")/("run}\right)$

The formula is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

The points are (2,2)" as $\left({x}_{1} , {y}_{1}\right) \text{ and } \left(5 , 8\right)$ as $\left({x}_{2} , {y}_{2}\right)$

$m = \frac{8 - 2}{5 - 2} = \frac{6}{3} = 2$

May 24, 2017

$m = 2$

#### Explanation:

The slope formula determines a slope from two points.

It says that given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$, you find the slope from:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

If we let $\left(2 , 2\right) = \left({x}_{1} , {y}_{1}\right)$ and $\left(5 , 8\right) = \left({x}_{2} , {y}_{2}\right)$, then we can plug these values into the slope formula.

Note that it does not matter which of the two points you decide to be the "first" or the "second".

$m = \frac{8 - 2}{5 - 2} = \frac{6}{3} = 2$