Plotting graphs from a table of values

Every graph starts with a table of values. A few special lines are worth knowing on sight.

Practise this lesson free (6 questions)

Table of values

Choose some x values, work out y for each, then plot the points (x, y) and join them.
Straight-line graphs: use a ruler. Quadratics: join with a smooth curve, not straight segments.
x−10123
y = x2 − 2x − 30−3−4−30

Special lines

x = 4 is a vertical line through 4 on the x-axis.
y = −2 is a horizontal line through −2 on the y-axis.
y = x goes diagonally up through the origin; y = −x goes diagonally down.
The x-axis is y = 0 and the y-axis is x = 0.

Lines like 3x + 2y = 12

Use the cover-up method. Put x = 0: 2y = 12, so y = 6. Put y = 0: 3x = 12, so x = 4.
Plot (0, 6) and (4, 0) and join them with a ruler.
Worked example

Complete the table for y = 3x − 1 for x = −1, 0, 1, 2.

  1. x = −1: 3 × (−1) − 1 = −4
  2. x = 0: −1
  3. x = 1: 2
  4. x = 2: 5

Answer: y = −4, −1, 2, 5

Key idea

Make a table, plot, then join with a ruler (straight line) or a smooth curve (quadratic). x = a is vertical, y = b is horizontal. For ax + by = c, put x = 0 then y = 0.

Quick check

Try two quick questions

See if it has sunk in. Answers are marked straight away.

Extra practice

2 more questions

Try each one, then tap to check.

  1. y = −5x + 6. Find y when x = −4.

    Show the answer

    Answer: 26

    −5 × (−4) + 6 = 26.

  2. Which line is horizontal?

    1. y = −x
    2. x = −1
    3. y = x
    4. y = −1
    Show the answer

    Answer: y = −1

    y = −1: every point has the same y-value, so it is flat.

Check you have got it

Answer 6 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.

Practise this lesson free (6 questions)All GCSE and International GCSE Mathematics lessons

Video for this lesson coming soon. Subscribe on YouTube

Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

Related lessons