Worked examples
The question
Question: graph y = 2x + 1 using a table of values.
y = 2x + 1
We pick some x values.
We work out y for each one.
Each x and y make a point.
1 Choose x values
We pick three easy x values: −1, 0 and 1.
Two points make a line.
The third one checks them.
2 Work out y
Put x = −1 in.
We get y = −1.
x = −1: y = 2(−1) + 1 = −2 + 1 = −1
−1
Now x = 0 in.
We get y = 1.
x = 0: y = 2(0) + 1 = 0 + 1 = 1
1
Now x = 1 in.
We get y = 3.
x = 1: y = 2(1) + 1 = 2 + 1 = 3
3
3 Plot the points
Draw the grid.
Each column is a point: x on top, y under it.
The first one is (−1, −1).
Put a dot.
(0, 1).
Dot.
Careful!
The x on top comes first, then the y under it: (0, 1).
Many people write the y first.
Careful: not (1, 0) ✗
(1, 3).
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 = 2.
We get y = 5.
x = 2: y = 2(2) + 1 = 4 + 1 = 5
The point (2, 5) 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.
▶ Watch it solved
The question
Question: graph y = −2x + 3 using a table of values.
y = −2x + 3
We pick some x values.
We work out y for each one.
Each x and y make a point.
1 Choose x values
We pick three easy x values: −1, 0 and 1.
Two points make a line.
The third one checks them.
2 Work out y
Put x = −1 in.
We get y = 5.
x = −1: y = −2(−1) + 3 = 2 + 3 = 5
Careful!
Minus times minus is plus.
−2 × (−1) is 2, not −2.
Careful: not −2 × (−1) = −2 ✗
5
Now x = 0 in.
We get y = 3.
x = 0: y = −2(0) + 3 = 0 + 3 = 3
3
Now x = 1 in.
We get y = 1.
x = 1: y = −2(1) + 3 = −2 + 3 = 1
1
3 Plot the points
Draw the grid.
Each column is a point: x on top, y under it.
The first one is (−1, 5).
Put a dot.
(0, 3).
Dot.
(1, 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 = 2.
We get y = −1.
x = 2: y = −2(2) + 3 = −4 + 3 = −1
The point (2, −1) 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.
▶ Watch it solved
The question
Question: graph y = (1/2)x + 1 using a table of values.
y = 12x + 1
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 2 at the bottom.
So we pick x values that 2 goes into: −2, 0 and 2.
Then y comes out whole.
x = −2, 0, 2: 2 goes in
Two points make a line.
The third one checks them.
2 Work out y
Put x = −2 in.
We get y = 0.
x = −2: y = 12(−2) + 1 = −1 + 1 = 0
0
Now x = 0 in.
We get y = 1.
x = 0: y = 12(0) + 1 = 0 + 1 = 1
1
Now x = 2 in.
We get y = 2.
x = 2: y = 12(2) + 1 = 1 + 1 = 2
2
3 Plot the points
Draw the grid.
Each column is a point: x on top, y under it.
The first one is (−2, 0).
Put a dot.
Careful!
The x on top comes first, then the y under it: (−2, 0).
Many people write the y first.
Careful: not (0, −2) ✗
(0, 1).
Dot.
(2, 2).
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 = 4.
We get y = 3.
x = 4: y = 12(4) + 1 = 2 + 1 = 3
The point (4, 3) 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.
▶ Watch it solved
