Step by step
The question
Question: find the slope of the line through (2, −5) and (−2, 3).
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: (−2, 3)
and (2, −5).
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 = −2 to x = 2 is 4.
Rise: how far we go up or down.
From y = 3 to y = −5 we go down 8.
Down counts as minus, so the rise 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 (2, −5).
The first point is (−2, 3).
Taking away a negative is the same as adding.
So it becomes (−5 − 3)/(2 + 2).
−5 minus 3 is −8.
2 plus 2 is 4.
The same rise and run as on the grid.
−8 divided by 4 is −2.
So m = −2.
A negative slope goes down from left to right.
For every 1 step to the right, it goes down 2.
4 Check
Let's check: take the points the other way round.
3 − (−5) is 8.
−2 − 2 is −4.
Plus over minus is minus.
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.