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Linear from an equation, step by step

An equation is linear when x is only multiplied by a number and added to.

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The question

Linear or nonlinear?

y = 10x² + 37

y = 10x² + 37
y = 10x² + 37
Linear or nonlinear?Nonlinear
  1. Linear means the graph is a straight line, and one thing decides it: what is being DONE to x. Multiplied by a number and added to — that is a line. Anything else is not.
  2. Look at what x is carrying: it is squared. Squaring is not multiplying by a fixed number — going from x = 1 to 2 to 3 gives 1, 4, 9, and those gaps are 3 then 5.
  3. So equal steps in x do NOT give equal steps in y: x is squared, so the steps in y grow as x grows. The graph curves, so it is not a line.

How it works.

  1. 01

    Linear means the graph is a straight line, and one thing decides it: what is being DONE to x. Multiplied by a number and added to — that is a line. Anything else is not.

  2. 02

    Look at what x is carrying: it is squared. Squaring is not multiplying by a fixed number — going from x = 1 to 2 to 3 gives 1, 4, 9, and those gaps are 3 then 5.

  3. 03

    So equal steps in x do NOT give equal steps in y: x is squared, so the steps in y grow as x grows. The graph curves, so it is not a line.

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