Graphing simple relationships | Year 7

01 / LEARN

The idea, step by step

Make a table before drawing

Put the input on the horizontal axis and the output on the vertical axis. Label both quantities, include units and use equal spacing for equal numerical changes.

If notebooks cost 4 dollars each, $C = 4 n$ . Since n counts whole notebooks, plot separate points for n=0,1,2,3,... .

Notebook prices
Notebooks n	Cost C (dollars)
0	0
1	4
2	8
3	12
4	16

Connect the graph to the situation

Read each plotted point back as an ordered pair. Join points only when intermediate inputs are possible and the model supports the connecting values.

A container starting with water 2 cm deep and rising steadily by 3 cm each minute has $d = 3 t + 2$ . Its depth can be modelled between whole-minute readings.

A common trap

Labelling axes only x and y without explaining quantities or units.

Instead: Name both contextual quantities and include their units.

02 / WORKED EXAMPLES

See the thinking

Example 1

Graph a counted quantity

Plot notebook cost for 0 to 4 notebooks.

Use notebook count horizontally and dollars vertically.
Plot (0,0),(1,4),(2,8),(3,12),(4,16).
Leave them as separate points because the model sells whole notebooks.

Each extra notebook adds 4 dollars.

Example 2

Read a continuous model

A depth model is $d = 3 t + 2$ , where t is minutes and d is centimetres. Explain (4,14).

The first coordinate gives 4 minutes.
The second gives 14 cm.
Check 3×4+2=14.

After 4 minutes the water is 14 cm deep.

Check your understanding

For $C = 2 d + 5$ , where d is kilometres and C is dollars, explain (3,11).

Show answer

A 3 km trip costs 11 dollars.

The input is distance; 2×3+5=11.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

For $C = 3 n$ , find costs for 0,1,2,3 tickets.
2 marks
Plot the pairs for $C = 3 n$ at n=0,1,2,3.
3 marks
For $h = 2 t + 4$ , where t is weeks and h is cm, find the height at t=3.
2 marks
For the same plant model, explain (2,8).
2 marks
A horizontal axis uses the same physical gap for 0 to 1 and for 1 to 5. Explain the error.
3 marks
A steady filling model gives depths 1,4,7,10 cm at times 0,1,2,3 min. Plot and join the points.
3 marks

Read the worked solutions

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

For $C = 3 n$ , find costs for 0,1,2,3 tickets.
2 marks
Multiply each count by 3.
0,3,6,9 dollars.
Plot the pairs for $C = 3 n$ at n=0,1,2,3.
3 marks
Label tickets on the horizontal axis and dollars vertically.
Only whole-ticket inputs are allowed.
(0,0),(1,3),(2,6),(3,9), as separate points.
For $h = 2 t + 4$ , where t is weeks and h is cm, find the height at t=3.
2 marks
2×3+4=10.
10 cm.
For the same plant model, explain (2,8).
2 marks
Read time first and height second.
At 2 weeks the model predicts 8 cm.
A horizontal axis uses the same physical gap for 0 to 1 and for 1 to 5. Explain the error.
3 marks
The first gap represents 1 unit; the next represents 4 units.
An ordinary uniform scale needs equal numerical changes in equal physical gaps.
A steady filling model gives depths 1,4,7,10 cm at times 0,1,2,3 min. Plot and join the points.
3 marks
The depth increases by 3 cm per minute.
Steady filling justifies intermediate depths.
(0,1),(1,4),(2,7),(3,10), joined by a straight segment.

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Curriculum reference & lesson scope

Australian Curriculum v9.0 / South Australian Curriculum

Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.

Official curriculum source ↗

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