Step by step
The question
Question: find the slope of the line through (1, −2) and (6, 1).
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, −2)
and (6, 1).
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 = 6 is 5.
Rise: how far we go up.
From y = −2 to y = 1 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 (6, 1).
The first point is (1, −2).
Taking away a negative is the same as adding.
So it becomes (1 + 2)/(6 − 1).
1 plus 2 is 3.
6 minus 1 is 5.
The same rise and run as on the grid.
This fraction is as simple as it gets.
So m = 3/5.
A positive slope goes up from left to right.
For every 5 steps to the right, it goes up 3.
4 Check
Let's check: take the points the other way round.
−2 − 1 is −3.
1 − 6 is −5.
Minus over minus is plus.
We get 3/5 again.
The same slope!
Let's look back.
First: plot the points.
Then: rise and run.
Then: use the formula.
Last: check.