Step by step
The question
Question: find the slope of the line through (1, 2) and (4, 11).
There are four choices.
First we solve it, the normal way.
Then we pick.
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 (4, 11).
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 = 4 is 3.
Rise: how far we go up.
From y = 2 to y = 11 is 9.
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.
It gives the same rise and run, without counting on the grid.
Put the numbers in.
The second point is (4, 11).
The first point is (1, 2).
11 minus 2 is 9.
4 minus 1 is 3.
The same rise and run as on the grid.
9 divided by 3 is 3.
So m = 3.
A positive slope goes up from left to right.
For every 1 step to the right, it goes up 3.
4 Check
Let's check: take the points the other way round.
2 − 11 is −9.
1 − 4 is −3.
Minus over minus is plus.
We get 3 again.
The same slope!
5 Pick the choice
Our answer is m = 3.
That is choice B.
6 Why not the others
A is 1/3.
Wrong: 3/9: run over rise, upside down.
C is 9.
Wrong: 11 − 2 = 9: forgot to divide by 4 − 1.
D is 13/3.
Wrong: 11 + 2: added the y numbers.
Let's look back.
First: plot the points.
Then: rise and run.
Then: use the formula.
Then: check.
Then: pick the choice.
Last: why not the others.