Linear vs Non Linear Functions

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What is a linear function?

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A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

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CCSS.8.F.A.3

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How can you identify a linear function?

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A linear function can be identified by its constant rate of change, meaning that the difference in y-values divided by the difference in x-values is the same for any two points.

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CCSS.HSF-LE.A.1B

Front

How can you identify a nonlinear function?

Back

A nonlinear function can be identified by its changing rate of change, meaning that the difference in y-values divided by the difference in x-values varies between points.

Tags

CCSS.8.F.A.3

Front

What is the general form of a linear equation?

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The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

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CCSS.8.EE.B.5

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What does the y-intercept represent in a linear function?

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The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

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Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2.

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CCSS.8.F.A.3

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What role do exponents play in identifying nonlinear functions?

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Exponents indicate that the function is nonlinear; for example, x^2 is nonlinear because it does not form a straight line.

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CCSS.8.F.A.3