Notice that this is the same as \(\dfrac{y_1-y_2}{x_1-x_2}\text{,}\) but it is not the same as \(\dfrac{y_2-y_1}{x_1-x_2}\text{.}\) In other words, you can subtract in either order you want, as long as you either start with both 1βs or both 2βs.
If we want to compute the slope of a line when we are given a graph, we can either pick two points on the line (any two points!) and compute slope using the formula we did before, or you can use another way of thinking about the slope formula:
Letβs pick the point \((0,-1)\) as our starting place, and then \((2,-4)\) as our ending point. Then, we rise \(-3\) (since we have to go down \(3\)) and run \(2\) (since we have to go to the right \(2\)). So, we can compute the slope as
Letβs pick the point \((-1,-3)\) as our starting place, and then \((0,1)\) as our ending point. Then, we rise \(4\) (since we have to go up \(4\)) and run \(1\) (since we have to go to the right \(1\)). So, we can compute the slope as