Step by step
The question
Question: find the slope of the line through (−5, 4) and (5, −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: (−5, 4)
and (5, −2).
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 = −5 to x = 5 is 10.
Rise: how far we go up or down.
From y = 4 to y = −2 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 (5, −2).
The first point is (−5, 4).
Taking away a negative is the same as adding.
So it becomes (−2 − 4)/(5 + 5).
−2 minus 4 is −6.
5 plus 5 is 10.
The same rise and run as on the grid.
We can make 6/10 simpler: divide top and bottom by 2.
The minus stays.
So m = −3/5.
A negative slope goes down from left to right.
For every 5 steps to the right, it goes down 3.
4 Check
Let's check: take the points the other way round.
4 − (−2) is 6.
−5 − 5 is −10.
Plus over minus is minus.
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.