Back to Interpret the equation y = mx + b as defining a linear function — Problem 2 · Task Set 47

8.F.A.3 Tutor Intake -- Linear vs. Nonlinear Functions

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Grade 8·7 problems·~8 min·Common Core Math - Grade 8·container·8-f-a-3

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Concepts

A function has a constant rate of change of 4: every time the
input increases by 1, the output increases by 4. Why must this
function's graph be a straight line?

Because the output is always positive.

Because equal horizontal steps always produce equal vertical steps, so the points line up in a consistent, uniform pattern.

Because the rate of change equals the y-intercept.

It doesn't have to be a straight line -- a constant rate of change just means it is a function, not that it is linear.