Question

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

Answer 1

You can use the gradient (slope) formula: `m=(y_2-y_1)/(x_2-x_1)`. In this case the slope is `-7/5`.

Explanation:

The slope of a line is often called '`m`', and is defined as `(rise)/(run)`: 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=(rise)/(run) = (y_2-y_1)/(x_2-x_1)`

We usually use the second point given to us in the question as `(x_2,y_2)` and the first as `(x_1,y_1)` 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 = (y_2-y_1)/(x_2-x_1) = (5-(-2))/(-2-3) = 7/(-5) = -7/5`

The slope of this line is `-7/5`.