Proportion Graphs · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading Proportion Graphs

Mathematics · Ratio & Proportion · ages 11-14
Name ______________________   Date ____________

  1. A directly proportional relationship always passes through the point (0, 0).

    Circle one:   True   False

  2. Why does a directly proportional graph always pass through (0, 0)?

    • Because every straight line passes through (0, 0)
    • Because when one quantity is zero, the other is zero too
    • Because the graph must stay flat
    • Because (0, 0) is the highest point

  3. A proportion graph passes through (2, 6). What is the value at 1?

    Answer: ______________

  4. A ratio table shows 2 kg of apples costs £6. Which point matches this on a graph, with kg on the x-axis and cost on the y-axis?

    1 kg32 kg63 kg9
    • (2, 6)
    • (6, 2)
    • (0, 6)

  5. Which table shows direct proportion?

    • 1 gives 2, 2 gives 3, 3 gives 4
    • 1 gives 2, 2 gives 4, 3 gives 7
    • 1 gives 2, 2 gives 4, 3 gives 6
    • 0 gives 1, 1 gives 2, 2 gives 3

  6. Mia says her proportional graph crosses the y-axis at (0, 2) instead of (0, 0). What does this tell you?

    • Her relationship is not directly proportional
    • She made the graph correctly
    • The rate is 2 per item

  7. 4 pens cost £3. How much do 10 pens cost? Give your answer in pounds.

    Answer: ______________

  8. A ratio table shows 3 tickets cost £12. Using the same rate, how much do 5 tickets cost?

    Answer: ______________

  9. Ben plots (2, 4) and (4, 8) for a proportional relationship, then draws a line through them but stops it before reaching zero. What is missing from his graph?

    • Adding more colour
    • Adding a third point above (4, 8)
    • Extending the line back through (0, 0)

  10. A line through the origin passes through (8, 20). What is y when x = 6?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_FspV_imUGK-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading Proportion Graphs W1-mt_FspV_imUGK-s1

  1. True · Zero amount always means zero of the other quantity, so (0, 0) is always on the line.
  2. Because when one quantity is zero, the other is zero too · Direct proportion means doubling one quantity doubles the other, so zero of one means zero of the other.
  3. 3 · The line goes through the origin with gradient 3, so at 1 the value is 3.
  4. (2, 6) · x is kilograms and y is cost, so 2 kg and £6 becomes the point (2, 6).
  5. 1 gives 2, 2 gives 4, 3 gives 6 · Only 1-2, 2-4, 3-6 multiplies every input by the same number, 2.
  6. Her relationship is not directly proportional · A directly proportional graph must start at (0, 0), so a graph starting at (0, 2) is not truly proportional.
  7. 7.5 · One pen costs £3 / 4 = £0.75, and 10 pens cost £7.50.
  8. 20 · The rate is £4 per ticket, so 5 tickets cost 5 times £4, which is £20.
  9. Extending the line back through (0, 0) · A proportional graph is a full straight line through the origin, not just the segment between the plotted points.
  10. 15 · The gradient is 20 / 8 = 2.5, and 2.5 x 6 = 15.
Worksheet · LightMySky