Year 7 - Tables of values and plotting points - Free practice

Year 7 Tables of Values and Plotting Points Worksheets & Practice

Build tables from patterns and rules, then plot them on the Cartesian plane.

Quick answer

How do you make a table of values and plot points on the Cartesian plane?

Choose x values, substitute each into the rule to find y, then write each pair as a coordinate (x, y). For example, y = 2x + 1 gives the pairs (0, 1), (1, 3), (2, 5). Plot each point by moving across the x-axis then up or down the y-axis, and the points will form a straight line.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 7 tables of values and plotting points: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Completing a table of values
A function has the rule $y = 3x + 2$ . Complete the table of values for $x = 0, 1, 2, 3$ .

$x$ 0 1 2 3
$y$
Show worked solution
Key idea: Substitute each $x$ value into the rule to find the matching $y$ value.
1. $x = 0$ : $y = 3(0) + 2 = 2$
2. $x = 1$ : $y = 3(1) + 2 = 5$
3. $x = 2$ : $y = 3(2) + 2 = 8$
4. $x = 3$ : $y = 3(3) + 2 = 11$
$x$ 0 1 2 3
$y$ 2 5 8 11

Answer: $y$ values are 2, 5, 8, 11.
Example 2 · Writing ordered pairs and describing the relationship
A function has the rule $y = 2x - 1$ . Complete the table of values for $x = 0, 1, 2, 3$ , write each result as an ordered pair, and describe how $y$ changes as $x$ increases.

$x$ 0 1 2 3
$y$
Show worked solution
Key idea: Substitute each $x$ value into the rule, record the $y$ value, then write each pair as $(x, y)$ .
1. $x = 0$ : $y = 2(0) - 1 = -1$ , giving $(0, -1)$
2. $x = 1$ : $y = 2(1) - 1 = 1$ , giving $(1, 1)$
3. $x = 2$ : $y = 2(2) - 1 = 3$ , giving $(2, 3)$
4. $x = 3$ : $y = 2(3) - 1 = 5$ , giving $(3, 5)$
5. Each time $x$ increases by $1$ , $y$ increases by $2$ , so $y$ grows at a constant rate.
Answer: $(0, -1),\ (1, 1),\ (2, 3),\ (3, 5)$ ; $y$ increases by $2$ each time $x$ increases by $1$ .
Example 3 · Real-life table of values and graph
Mia is saving money. She starts with $5 and earns $3 for each chore she completes. The rule for her total savings $y$ (in dollars) after completing $x$ chores is $y = 3x + 5$ . Complete the table of values for $x = 0, 1, 2, 3, 4$ , write each result as an ordered pair, and describe how her savings change.
Show worked solution
Key idea: Substitute each $x$ value into $y = 3x + 5$ to find Mia's savings after that many chores.
1. $x = 0$ : $y = 3(0) + 5 = 5$ , giving $(0, 5)$
2. $x = 1$ : $y = 3(1) + 5 = 8$ , giving $(1, 8)$
3. $x = 2$ : $y = 3(2) + 5 = 11$ , giving $(2, 11)$
4. $x = 3$ : $y = 3(3) + 5 = 14$ , giving $(3, 14)$
5. $x = 4$ : $y = 3(4) + 5 = 17$ , giving $(4, 17)$
6. Mia's savings increase by $3 for each extra chore completed.
Answer: $(0, 5),\ (1, 8),\ (2, 11),\ (3, 14),\ (4, 17)$ ; savings increase by $3 per chore.

$x$	0	1	2	3
$y$

$x$	0	1	2	3
$y$	2	5	8	11

$x$	0	1	2	3
$y$

Common mistakes

Where students usually lose marks

Forgetting to apply the whole rule

For $y = 3x + 2$ at $x = 4$ : student writes $y = 3 + 2 = 5$ instead of $y = 3(4) + 2 = 14$ .

Always multiply the coefficient by the $x$ value first, then add or subtract the constant. Write out the substitution step fully before simplifying.

Mixing up the order in an ordered pair

Student writes the $y$ value first, for example $(5, 2)$ instead of $(2, 5)$ .

An ordered pair is always $(x, y)$ : the horizontal value first, then the vertical value. Think of it as reading left to right, just like the axes.

Sign errors with negative results

For $y = 2x - 1$ at $x = 0$ : student writes $y = 0$ instead of $y = -1$ .

When $x = 0$ the $x$ term disappears, leaving only the constant. If the constant is negative, the answer is negative. Check by reading the rule carefully with $x$ replaced by $0$ .

Plotting points with axes swapped

For the point $(3, 7)$ , student moves $7$ units across and $3$ units up.

Always move horizontally first (the $x$ value) and then vertically (the $y$ value). Labelling both axes before you start plotting helps avoid this swap.

Try one yourself

Your turn

Complete the table of values for the rule $y = 3x - 2$ using $x = 0, 1, 2, 3, 4$ . What is the $y$ -value when $x = 4$ ?

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About this worksheet

Why we built it

Tables of values and plotting points is where Year 7 students first connect algebraic rules to visual graphs. These worksheets guide students from reading a pattern or function rule, completing a table of x and y values, and then accurately plotting those coordinates on the Cartesian plane. Worked solutions accompany every question so students can check exactly where their thinking or plotting went wrong.

What's covered

Sub-skills your student will practise

✓Completing tables of values from a function rule such as y = 2x + 1
✓Identifying and extending visually changing patterns to generate values
✓Writing coordinates as ordered pairs from a completed table
✓Plotting ordered pairs accurately on the Cartesian plane
✓Describing the relationship shown by a set of plotted points
✓Connecting a table of values to its graph and back again

From our families

Parents on the practice questions.

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Year 8 · Maths

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Year 10 · Maths

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Frequently asked

Questions parents ask about tables of values and plotting points

What is a table of values in Year 7 maths?

A table of values lists inputs (x) and their matching outputs (y) for a rule or pattern. For example, the rule y = 2x + 1 gives the pairs (0, 1), (1, 3), (2, 5) and so on. Building the table is the first step before drawing a graph.

How do I help my child plot points on the Cartesian plane?

Remind them to always go along the x-axis first, then up or down the y-axis. A common saying is 'along the corridor, then up the stairs'. Checking that the plotted points form a straight line or a clear pattern is a good way to catch any errors.

What kinds of patterns appear in the Year 7 curriculum for this topic?

Students work with both visual patterns (like growing dot or tile arrangements) and function rules written with variables. They describe how the output changes as the input increases, and they connect that description to the shape of the graph.

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