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Linear from a table, step by step

A table is linear when equal steps in x bring equal steps in y.

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The question
x0369y52377167LinearNonlinear

Linear or nonlinear?

x: 0, 3, 6, 9 y: 5, 23, 77, 167

x0369y52377167
x0369steps333
y52377167steps185490
Linear or nonlinear?Nonlinear
  1. A straight line climbs by the same amount every time. So this is not a question about the numbers themselves — it is a question about the STEPS between them.
  2. First check the x row, because the rest only means anything if these are even: 3, 3, 3. Every step is 3, so the readings are evenly spaced.
  3. Now take the steps in y: 18, 54, 90.
  4. The steps are not all the same, so the points bend instead of climbing steadily: x goes up by 3 every time, but the steps in y are 18, 54, 90 — they change, so the points do not lie on a line.

How it works.

  1. 01

    A straight line climbs by the same amount every time. So this is not a question about the numbers themselves — it is a question about the STEPS between them.

  2. 02

    First check the x row, because the rest only means anything if these are even: 3, 3, 3. Every step is 3, so the readings are evenly spaced.

  3. 03

    Now take the steps in y: 18, 54, 90.

  4. 04

    The steps are not all the same, so the points bend instead of climbing steadily: x goes up by 3 every time, but the steps in y are 18, 54, 90 — they change, so the points do not lie on a line.

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