Step by step
The question
Question: find the slope of the line through (0, 1) and (4, 4).
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: (0, 1)
and (4, 4).
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 = 0 to x = 4 is 4.
Rise: how far we go up.
From y = 1 to y = 4 is 3.
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, 4).
The first point is (0, 1).
4 minus 1 is 3.
4 minus 0 is 4.
The same rise and run as on the grid.
This fraction is as simple as it gets.
So m = 3/4.
A positive slope goes up from left to right.
For every 4 steps to the right, it goes up 3.
4 Check
Let's check: take the points the other way round.
1 − 4 is −3.
0 − 4 is −4.
Minus over minus is plus.
We get 3/4 again.
The same slope!
Let's look back.
First: plot the points.
Then: rise and run.
Then: use the formula.
Last: check.