# What is the slope of the line passing through the following points:  (-3, -1) ; (2,3)?

Feb 29, 2016

$m = \frac{4}{5}$

#### Explanation:

The slope of a line is generally its "rise over run". In this case, it is the number of units the line goes up or down over the distance it travels along the $x$-axis.

In this example, given the two points we would be able to compute for the slope of the line by assigning one point as ${P}_{1}$ and the other as ${P}_{2}$. Now we subtract the $y$-component of ${P}_{1}$ from ${P}_{2}$ then divide it by the difference of the $x$-components of ${P}_{2}$ and ${P}_{1}$. So this is the equation for finding the slope from two points:

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

Where m is the slope and ${y}_{2}$ and ${y}_{1}$ as the $y$-components and ${x}_{2}$ and ${x}_{1}$ as the $x$-components that I mentioned earlier.

Computing for the value of the slope...

[Solution]
let:
${P}_{1} : \left(- 3 , - 1\right)$
${P}_{2} : \left(2 , 3\right)$

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

$m = \frac{3 - \left(- 1\right)}{2 - \left(- 3\right)}$
$m = \frac{3 + 1}{2 + 3}$
$m = \frac{4}{5}$