Step by step
The question
Question: find the slope of the line through (−1, 4) and (3, 12).
1 Plot the points
Draw the grid: the x-axis goes across, and the y-axis goes up and down.
They meet at 0, a point called the origin.
Put both points on the grid: (−1, 4)
and (3, 12).
Draw the line through them.
2 Rise and run
We start at the point on the left.
Run: how far we go right.
From x = −1 to x = 3 is 4.
Rise: how far we go up.
From y = 4 to y = 12 is 8.
3 Use the formula
We call the slope m.
m = rise over run.
The top is the change in y: second y minus first y.
The bottom is the change in x: second x minus first x.
It gives the same rise and run, without counting on the grid.
Put the numbers in.
The second point is (3, 12).
The first point is (−1, 4).
Taking away a negative is the same as adding.
So it becomes (12 − 4)/(3 + 1).
12 minus 4 is 8.
3 plus 1 is 4.
The same rise and run as on the grid.
8 divided by 4 is 2.
So m = 2.
A positive slope goes up from left to right.
For every 1 step to the right, it goes up 2.
4 Check
Let's check: take the points the other way round.
4 − 12 is −8.
−1 − 3 is −4.
Minus over minus is plus.
We get 2 again.
The same slope!
Let's look back.
First: plot the points.
Then: rise and run.
Then: use the formula.
Last: check.