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

Straight lines from log plots

Mathematics · Algebra · ages 17-18
Name ______________________   Date ____________

  1. A log-log plot passes through (log x = 2, log y = 1) and (log x = 4, log y = 7). What is the gradient?

    Answer: ______________

  2. Data are thought to follow y = a x^n. Which plot should give a straight line?

    • log y against log x
    • y against x
    • log y against x
    • x against log y

  3. Data should follow y = a x^n. Which plot gives a straight line?

    • log y against log x
    • log y against x
    • y against x

  4. A log-log plot passes through (log x = 2, log y = 1) and (log x = 4, log y = 7). What is the gradient?

    Answer: ______________

  5. A base 10 log-log plot of data following y = a x^n has intercept 3. What is a?

    Answer: ______________

  6. A base 10 log-log plot has gradient 1/2 and intercept 0. Which model fits?

    • y = sqrt(x)
    • y = x^2
    • y = 2x

  7. A base 10 log-log plot of y = a x^n has intercept 2 on the log y axis. What is a?

    • 20
    • 2
    • 100
    • 200

  8. Tom says a log-log plot of y = a x^2 has gradient 2 no matter what a is. Is Tom right?

    Circle one:   True   False

  9. A straight log y against x plot with negative gradient means b < 1 in y = a b^x with a > 0. True or false?

    Circle one:   True   False

  10. A base 10 log-log plot has gradient 1/2 and intercept 0. Which model fits?

    • y = x^2
    • y = sqrt(x)
    • y = 2x
    • y = 10^x
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Answer key

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

Straight lines from log plots W1-mt_TVar2jxRMI-s1

  1. 3 · The gradient is 3. Rise 6 over run 2 gives 3, which is the power n.
  2. log y against log x · Plot log y against log x. Taking logs gives log y = log a + n log x, which is linear in log x.
  3. log y against log x · Logs give log y = log a + n log x, which is linear in log x. So plot log y against log x.
  4. 3 · Rise 6 over run 2 gives 3. That gradient is the power n.
  5. 1000 · a = 1000. The intercept is log a, so a = 10 cubed.
  6. y = sqrt(x) · Gradient 1/2 is the power and intercept 0 gives a = 1. So the model is y = sqrt(x).
  7. 100 · a = 100. The intercept equals log a, and 10 squared is 100.
  8. True · Tom is right. The gradient equals the power n = 2, while a only shifts the intercept.
  9. True · The gradient is log b, and a negative log means b sits below 1. The sentence is true.
  10. y = sqrt(x) · y = sqrt(x). The gradient 1/2 is the power and intercept 0 gives a = 1.
Worksheet · LightMySky