🔮 Algebra Realm · Graphs

Tables of values

Tables of values focuses on how to organise substituted outputs so a graph can be plotted systematically. In this lesson, focus on straight-line graphs connect coordinates, rates and equations.

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Understand Tables of values

Tables of values focuses on how to organise substituted outputs so a graph can be plotted systematically. In this lesson, focus on straight-line graphs connect coordinates, rates and equations.

Straight-line graphs connect coordinates, rates and equations. Gradient measures vertical change per horizontal step; the y-intercept records the value when x is zero. For tables of values, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Tables of values: Straight-line graphs connect coordinates, rates and equations. Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Keep the tables of values representation visible until the final line.

Picture the idea

Plot draggable points on a coordinate plane, draw the line and compare its rise, run and axis crossing. Use the model to explain one change you notice while working on tables of values.

Check as you go

Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Write that check beside the final tables of values answer.

Key vocabulary

coordinategradienty-interceptaxislinear relationshiptablesvalues

Rules and key facts

For y = x + 2, x values -1, 0, 1 give y values 1, 2, 3.

  • Label and read both axes.
  • Plot or identify ordered pairs as x first, then y.
  • Use rise divided by run for gradient or read the y-axis crossing for intercept.
  • Check the relationship with a second point or a table value. Record the check explicitly for tables of values.

Step-by-step method

  1. Label and read both axes.
  2. Plot or identify ordered pairs as x first, then y.
  3. Use rise divided by run for gradient or read the y-axis crossing for intercept.
  4. Check the relationship with a second point or a table value. Record the check explicitly for tables of values.

What you need first

  • Recognise the vocabulary: coordinate, gradient, y-intercept.
  • Be able to explain the purpose of tables of values before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Travel graphs
  • Fixed fees and rates

Visual / interactive

See the idea, then move it around

Skip to Practice

Plot draggable points on a coordinate plane, draw the line and compare its rise, run and axis crossing. Use the model to explain one change you notice while working on tables of values.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
Responsive · validated · topic linked

Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Tables of values — For y = 3x + 2, find y when x = 2. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 2: y = 3 × 2 + 2 = 8. Final answer: 8. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Label and read both axes.
  2. Plot or identify ordered pairs as x first, then y.
  3. Use rise divided by run for gradient or read the y-axis crossing for intercept.
Secure example

Use the normal method

Given information: Tables of values — For y = 3x + 14, find y when x = 10. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 10: y = 3 × 10 + 14 = 44. Final answer: 44. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Plot the resulting coordinate pairs if requested.

Challenge example

Stretch the idea

Given information: Tables of values — For y = 3x + 13, find y when x = 7. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 7: y = 3 × 7 + 13 = 34. Final answer: 34. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Tables of values — For y = 3x + 12, find y when x = 4. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 4: y = 3 × 4 + 12 = 24. Final answer: 24. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Show one substitution outside the table as evidence.

Common mistakes

  • Reading coordinates in the wrong order. This is a key trap when answering tables of values questions.
  • Using horizontal change divided by vertical change for gradient.

How to check your answer

Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Write that check beside the final tables of values answer.

Extension challenge

Create a tables of values problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Tables of values challenge

Use plot patrol controls to solve three checked tables of values rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Challenge Tables of values Arcane Boss

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Study cards

Core idea

Tables of values: Straight-line graphs connect coordinates, rates and equations. Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Keep the tables of values representation visible until the final line.

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Key vocabulary

coordinate · gradient · y-intercept · axis · linear relationship · tables · values

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Rules

Label and read both axes. Plot or identify ordered pairs as x first, then y. Use rise divided by run for gradient or read the y-axis crossing for intercept. Check the relationship with a second point or a table value. Record the check explicitly for tables of values.

Tap to mark reviewed
Formula / fact

For y = x + 2, x values -1, 0, 1 give y values 1, 2, 3.

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Foundation example

Given information: Tables of values — For y = 3x + 2, find y when x = 2. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 2: y = 3 × 2 + 2 = 8. Final answer: 8. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Tables of values — For y = 3x + 14, find y when x = 10. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 10: y = 3 × 10 + 14 = 44. Final answer: 44. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Tables of values — For y = 3x + 13, find y when x = 7. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 7: y = 3 × 7 + 13 = 34. Final answer: 34. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Tables of values — For y = 3x + 12, find y when x = 4. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 4: y = 3 × 4 + 12 = 24. Final answer: 24. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Reading coordinates in the wrong order. This is a key trap when answering tables of values questions.

Tap to mark reviewed
Exam tip

For tables of values, show the key representation before the final calculation. Use this final check: Substitute one plotted coordinate into the equation or count a second rise-and-run triangle.

Tap to mark reviewed
Real-world use

Travel graphs, Fixed fees and rates

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Checklist

I can explain tables of values, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Tables of values

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Simple explanation

Tables of values: Straight-line graphs connect coordinates, rates and equations. Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Keep the tables of values representation visible until the final line.

Think of tables of values as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Label and read both axes.
  2. Plot or identify ordered pairs as x first, then y.
  3. Use rise divided by run for gradient or read the y-axis crossing for intercept.
  4. Check the relationship with a second point or a table value. Record the check explicitly for tables of values.

Hint 1

Start by naming the given information and the exact result required for tables of values.

Hint 2

Label and read both axes.

Full worked solution

Given information: Tables of values — For y = 3x + 2, find y when x = 2. Method choice: use the tables of values method and show each step with the stated values. Calculation or reasoning: Substitute x = 2: y = 3 × 2 + 2 = 8. Final answer: 8. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Label and read both axes. → Plot or identify ordered pairs as x first, then y. → Use rise divided by run for gradient or read the y-axis crossing for intercept. → Check the relationship with a second point or a table value. Record the check explicitly for tables of values.

Common mistake warning

Reading coordinates in the wrong order. This is a key trap when answering tables of values questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain tables of values in my own words.
  • I can use these words accurately: coordinate, gradient, y-intercept.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Reading coordinates in the wrong order.
  • I can apply this check: Substitute one plotted coordinate into the equation or count a second rise-and-run triangle.
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