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