Step by step
The question
Question: find the slope of the line through (4, −3) 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 (4, −3).
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 = 4 is 6.
Rise: how far we go up.
From y = −3 to y = −3 is 0.
We do not go up at all.
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 (4, −3).
The first point is (−2, −3).
Taking away a negative is the same as adding.
So it becomes (−3 + 3)/(4 + 2).
−3 plus 3 is 0.
4 plus 2 is 6.
The same rise and run as on the grid.
0 divided by 6 is 0.
So m = 0.
A slope of 0 means a flat line.
The line does not go up or down.
4 Check
Let's check: take the points the other way round.
−3 − (−3) is 0.
−2 − 4 is −6.
We get 0 again.
The same slope!
Let's look back.
First: plot the points.
Then: rise and run.
Then: use the formula.
Last: check.