Step by step
The question
Question: graph y = (1/3)x − 2 using a table of values.
We pick some x values.
We work out y for each one.
Each x and y make a point.
1 Choose x values
The slope has 3 at the bottom.
So we pick x values that 3 goes into: −3, 0 and 3.
Then y comes out whole.
Two points make a line.
The third one checks them.
2 Work out y
Put x = −3 in.
We get y = −3.
Now x = 0 in.
We get y = −2.
Now x = 3 in.
We get y = −1.
3 Plot the points
Draw the grid.
Each column is a point: x on top, y under it.
The first one is (−3, −3).
Put a dot.
(0, −2).
Dot.
Careful!
The x on top comes first, then the y under it: (0, −2).
Many people write the y first.
(3, −1).
Dot.
4 Draw the line
The three dots line up.
Join the dots with a straight line.
It keeps going both ways.
5 Check
Let's check with one more x: x = 6.
We get y = 0.
The point (6, 0) is on our line.
So the graph is right!
Let's look back.
First: choose x values.
Then: work out y.
Then: plot the points.
Then: draw the line.
Last: check.