Linear vs. Nonlinear

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What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. It has a variable rate of change.

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CCSS.8.F.A.3

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How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference between the y-values for equal increments in the x-values.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the slope of a linear function?

Back

The slope of a linear function is the rate of change, representing how much y changes for a unit change in x.

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CCSS.8.EE.B.5

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What does it mean if a function has a constant rate of change?

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It means that for every equal increase in x, the increase in y is always the same, indicating a linear relationship.

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CCSS.HSF-LE.A.1B

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What is the y-intercept of a linear function?

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The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, b) where b is the y-value.

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Can a linear function have a curved graph?

Back

No, a linear function cannot have a curved graph; if the graph is curved, it is a nonlinear function.

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CCSS.8.F.A.3

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which creates a parabola when graphed.

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CCSS.8.F.A.3

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What is the difference between a linear equation and a nonlinear equation?

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A linear equation can be written in the form y = mx + b, while a nonlinear equation cannot be expressed in this form.

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CCSS.8.F.A.3

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How do you determine if a function is linear or nonlinear from its equation?

Back

If the equation can be simplified to the form y = mx + b, it is linear; otherwise, it is nonlinear.

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CCSS.8.F.A.3