Tables and straight-line graphs | Year 8

01 / LEARN

The idea, step by step

Make a table before plotting

Choose inputs, substitute each into the rule, and pair each input with its output. An ordered pair records horizontal position first. Include zero and values on either side when the domain allows them.

Calculate at least three points. Linear-rule points align, so a stray point gives a useful warning of an arithmetic or plotting error.

Respect the context and scale

Label both axes and mark evenly spaced values along each one. Plot each pair, then use a ruler for a continuous relationship. Different axis scales can change how steep the same line appears.

Counts such as tickets use whole-number inputs. They remain separate points even when a linear formula describes their values; a physical length may allow a continuous interval.

A common trap

Reversing the coordinates when plotting.

Instead: For $(2, 5)$ move 2 horizontally, then 5 vertically.

02 / WORKED EXAMPLES

See the thinking

Example 1

A table and graph

Graph $y = 2 x + 1$ using x = -2, -1, 0 and 1.

Values for the line
x	-2	-1	0	1
y	-3	-1	1	3

Substitute each input into $2 x + 1$ .
For x = -2, the output is $- 4 + 1 = - 3$ .
Plot with x horizontal and y vertical; the four points align.

Plot

(- 2, - 3), (- 1, - 1), (0, 1), (1, 3)

Example 2

A point check

Does $(3, 1)$ lie on $y = x - 2$ ?

Use the first coordinate x = 3.
The rule gives $y = 3 - 2 = 1$ .
This matches the second coordinate.

Yes.

Check your understanding

Find the point on $y = 3 x - 2$ at x = 2.

Show answer

$(2, 4)$ .

Substitution gives $y = 6 - 2 = 4$ .

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

For $y = x + 3$ , find outputs for x = -2, 0 and 2.
3 marks
For $y = 2 x - 1$ , find outputs for x = -1, 0 and 2.
3 marks
Is $(2, 7)$ on $y = 3 x + 1$ ?
2 marks
Is $(- 2, 1)$ on $y = - x + 1$ ?
2 marks
Draw $y = x - 1$ for $- 2 \leq x \leq 3$ using a table.
3 marks
Tickets cost AUD 4 each. Does the graph $C = 4 n$ for ticket purchases contain n = 1.5? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

For $y = x + 3$ , find outputs for x = -2, 0 and 2.
3 marks
Add 3 to each input.
The pairs are $(- 2, 1), (0, 3), (2, 5)$ .
1, 3 and 5.
For $y = 2 x - 1$ , find outputs for x = -1, 0 and 2.
3 marks
Double each input and subtract 1.
The pairs are $(- 1, - 3), (0, - 1), (2, 3)$ .
-3, -1 and 3.
Is $(2, 7)$ on $y = 3 x + 1$ ?
2 marks
Substituting x = 2 gives 7.
It matches the second coordinate.
Yes.
Is $(- 2, 1)$ on $y = - x + 1$ ?
2 marks
At x = -2, the output is 3.
The proposed output is 1.
No.
Draw $y = x - 1$ for $- 2 \leq x \leq 3$ using a table.
3 marks
Calculate three or more pairs.
Plot and join only over the stated interval.
A segment through $(- 2, - 3), (0, - 1), (3, 2)$ .
Tickets cost AUD 4 each. Does the graph $C = 4 n$ for ticket purchases contain n = 1.5? Explain.
2 marks
The input is a count of tickets.
Only non-negative whole-number inputs are realistic.
No, if tickets must be bought whole.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics (2026)

Multi-step equations; brackets and variables on both sides; equations with rational solutions; substitution checks; one-variable inequalities and number-line solutions; tables and straight-line graphs; horizontal/vertical lines; how coefficients change a graph; graphical solutions and intersection checks; real-world linear models with digital exploration.

Official curriculum source ↗

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