An equation is linear when x is only multiplied by a number and added to — anything squared, cubed or under a fraction bends. These free printable worksheets ask it of the equation alone.
If they get stuck
The answer key prints on a separate page.
One thing decides it: what is being done to x. y = 2x + 3 is a line; y = 2x² + 3 is not, because squaring x makes the graph curve. The standard's own example, A = s², is ruled out for the same reason — its points (1, 1), (2, 4), (3, 9) do not lie on a straight line. Reading the operation, not spotting a shape, is the whole skill here.
The trap on every sheet is y = 7. It has no x at all, so a child hunting for the mx + b form does not find one and answers nonlinear — but every point sits at the same height, which is a flat line, slope zero, not "no line". It is the most missed question on this standard, so no sheet leaves it out. This is the from-the-equation half of the topic; the table half is a separate page, because a table cannot be answered by recognizing a form.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Linear from an equation, step by step