Step by step
The question
Question: find the slope of the line through (−3, −1) and (1, 7).
1 Plot the points
Draw the grid.
The x-axis goes across.
The y-axis goes up and down.
They meet at 0.
That point is called the origin.
Put both points on the grid: (−3, −1)
and (1, 7).
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 = −3 to x = 1 is 4.
Rise: how far we go up.
From y = −1 to y = 7 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.
Put the numbers in.
The second point is (1, 7).
The first point is (−3, −1).
Taking away a negative is the same as adding.
So it becomes (7 + 1)/(1 + 3).
7 plus 1 is 8.
1 plus 3 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.
−1 − 7 is −8.
−3 − 1 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.