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  • Grade 8
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Linear or nonlinear worksheets

Linear means the graph is a straight line. These free printable worksheets ask it of an equation and of a table of values.

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Ready to printLinear or nonlinear
Linear or nonlinear worksheet — Equations and tables, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

One thing decides an equation: what is being done to x. Multiplied by a number and added to — that is a line. Squared, cubed, or sitting underneath a fraction, and it is not. The standard's own example is A = s², ruled out because its graph passes through (1, 1), (2, 4) and (3, 9), which are not on a straight line.

Why this sheet works

The trap on every equations sheet is y = 7. There is no x in it at all, so a child hunting for the mx + b shape does not find one and answers nonlinear — but every point sits at the same height, the graph is a flat line across the page, and flat is a slope of zero rather than no slope. It is the single most missed question on this standard, so no sheet here leaves it out.

How this one works

One question from this sheet, worked through a step at a time.

y = 3x² + 4

y = 3x² + 4
y = 3x² + 4
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.

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