Step by step
The question
Question: find the slope of the line through (1, 1) and (4, 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: (1, 1)
and (4, 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 = 1 to x = 4 is 3.
Rise: how far we go up.
From y = 1 to y = 7 is 6.
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 (4, 7).
The first point is (1, 1).
7 minus 1 is 6.
4 minus 1 is 3.
The same rise and run as on the grid.
6 divided by 3 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 −6.
1 − 4 is −3.
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.