Linear vs. Nonlinear

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What is a linear function?

Back

A linear function is a function that has a constant rate of change, which means that the graph of the function forms a straight line.

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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 have a constant rate of change, resulting in a graph that is not a straight line.

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CCSS.8.F.A.3

Front

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

Back

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

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much the y-value changes for a unit change in the x-value.

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CCSS.8.EE.B.5

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What is the y-intercept of a linear function?

Back

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.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which indicates that as the x-value increases, the y-value decreases.

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CCSS.8.EE.B.5

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which produces a parabolic graph.

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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 a graph?

Back

If the graph is a straight line, the function is linear; if the graph is curved, the function is nonlinear.

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CCSS.8.F.A.3

Front

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

Back

A linear equation represents a straight line, while a nonlinear equation represents a curve or other shapes.

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CCSS.8.F.A.3