Question

What is the slope of the line between (3,5) and (1, 3 )?

Answer 1

`1`

Explanation:

If a line passes through two points `(x_1, y_1)` and `(x_2, y_2)` then its slope `m` is given by the formula:

`m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)`

In our example, I would normally pick the points in the reverse order to the one you have specified in order to be working with positive numbers, like so:

`(x_1, y_1) = (1, 3)`

`(x_2, y_2) = (3, 5)`

`m = (y_2-y_1)/(x_2-x_1) = (5-3)/(3-1) = 2/2 = 1`

To demonstrate the the order of the points makes no difference to the result, let's see that with the points the other way round:

`(x_1, y_1) = (3, 5)`

`(x_2, y_2) = (1, 3)`

`m = (y_2-y_1)/(x_2-x_1) = (3-5)/(1-3) = (-2)/(-2) = 1`