Step by step
The question
Question: find the slope of the line through (2, 1) and (2, 5).
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, 1)
and (2, 5).
Draw the line through them.
2 Rise and run
The two points have the same x.
Run: how far we go right.
We do not go right at all: the run is 0.
Rise: how far we go up.
From y = 1 to y = 5 is 4.
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, 1).
5 minus 1 is 4.
2 minus 2 is 0.
The same rise and run as on the grid.
The bottom is 0.
We cannot divide by 0.
So there is no number for the slope.
We say the slope is undefined.
The line goes straight up and down.
Let's look back.
First: plot the points.
Then: rise and run.
Last: use the formula.