# What is the slope of the line passing through the following points:  (5, -2) ; (-2,-1)?

Dec 13, 2015

The slope of the line is $- \frac{1}{7}$.

#### Explanation:

In order to find the slope of a line passing through two points, use the slope formula:

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

$m$ stands for the slope of the line.
${x}_{1}$ and ${y}_{1}$ are the $x$ and $y$ coordinates of your first point.
${x}_{2}$ and ${y}_{2}$ are the $x$ and $y$ coordinates of your second point.

If you are wondering what I mean by first and second point, choose one of your two points to be the first point. It does not matter which point you choose.

From there, the other point that you did not choose is your second point.

For example, I chose (5, -2) to be my first point, and (-2, -1) to be my second point. I made this decision randomly.

To start solving for the slope, plug the x-coordinates and y-coordinates into their proper variables. In my case, my equation is now:

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

Next, simplify and solve the equation:

$m = \frac{- 1 + 2}{-} 7$

$m = - \frac{1}{7}$

The slope of the line is $- \frac{1}{7}$.