Linear vs. Nonlinear

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What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change, meaning the ratio of the change in y to the change in x is constant.

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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 form a straight line when graphed. The rate of change is not constant, meaning the ratio of the change in y to the change in x varies.

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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 y-values for equal differences in x-values.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

A nonlinear function will show varying differences in y-values for equal differences in x-values.

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CCSS.HSF-LE.A.1B

Front

What does it mean if a function is represented by a straight line on a graph?

Back

It means the function is linear, indicating a constant rate of change.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean if a function is represented by a curve on a graph?

Back

It means the function is nonlinear, indicating that the rate of change is not constant.

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CCSS.HSF-LE.A.1B

Front

What is the slope of a linear function?

Back

The slope is the measure of the steepness of the line, calculated as the change in y divided by the change in x.

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CCSS.8.EE.B.5

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3, which represents a straight line.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear function?

Back

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

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CCSS.8.F.A.3

Front

What is the significance of the y-intercept in a linear function?

Back

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