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