We are given a table that contains a number of points that lie on a line. We want to explain how we can find the slope of the line and then calculate the slope.
x
2
4
6
8
y
10
15
20
25
Looking at the table, we can identify 4 ordered pairs.
(2,10), (4,15), (6,20), (8,25)
Each of those pairs represent a single point that lies on the line. To find the slope m of the line, we select two points and use the Slope Formula.
m = y_2-y_1/x_2-x_1
Now let's find the slope by substituting (2,10) and (4,15) into the Slope Formula.
To remember the Slope Formula, recall that slope is rise over run.
m = rise/run
We can visualize this by looking at a graph of a line.
Now let's say that the first point has coordinates (x_1, y_1) and the second point has coordinates (x_2, y_2). Then, the run is the difference between the x-coordinates and the rise is the difference between the y-coordinates.
Now we can substitute y_2-y_1 for the rise and x_2 - x_1 for the run.
m = rise/run ⇒ m = y_2 - y_1/x_2 - x_1
We have received the Slope Formula.
