# How do you find the slope of (a line passing through the points) (3, -2) and (-2, 5)?

Feb 1, 2016

You can use the gradient (slope) formula: $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$. In this case the slope is $- \frac{7}{5}$.

#### Explanation:

The slope of a line is often called '$m$', and is defined as $\frac{r i s e}{r u n}$: the amount a line 'rises' vertically (in the $y$ direction) for each unit it 'runs' horizontally (in the $x$ direction).

A line with a slope of 2 rises by 2 units for every unit it moves onward in $x$, while a line with a slope of $- 3$ falls by 3 units in $y$ for each unit in $x$.

A formula for this is as follows:

$m = \frac{r i s e}{r u n} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

We usually use the second point given to us in the question as $\left({x}_{2} , {y}_{2}\right)$ and the first as $\left({x}_{1} , {y}_{1}\right)$ but it doesn't matter : try the experiment for yourself of doing it the other way around, and see that you get the same answer for the slope.

In this case:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{5 - \left(- 2\right)}{- 2 - 3} = \frac{7}{- 5} = - \frac{7}{5}$

The slope of this line is $- \frac{7}{5}$.