Step by step
The question
Question: find the slope of the line through (−6, −2) and (−1, −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: (−6, −2)
and (−1, −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 = −6 to x = −1 is 5.
Rise: how far we go up or down.
From y = −2 to y = −4 we go down 2.
Down counts as minus, so the rise is −2.
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 (−1, −4).
The first point is (−6, −2).
Taking away a negative is the same as adding.
So it becomes (−4 + 2) over (−1 + 6).
−4 plus 2 is −2.
−1 plus 6 is 5.
The same rise and run as on the grid.
This fraction is as simple as it gets.
So m = −2/5.
A negative slope goes down from left to right.
For every 5 steps to the right, it goes down 2.
4 Check
Let's check: take the points the other way round.
−2 − (−4) is 2.
−6 − (−1) is −5.
Plus over minus is minus.
We get −2/5 again.
The same slope!
Let's look back.
First: plot the points.
Then: rise and run.
Then: use the formula.
Last: check.