Question

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

Answer 1

`m = 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 = (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: (-3, -1)`
`P_2: (2,3)`

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (3 - (-1))/(2 - (-3))`
`m = (3+1)/(2+3)`
`m = 4/5`