Linear vs NonLinear Functions

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What is a linear function?

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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

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What is a nonlinear function?

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A nonlinear function is a function that does not create a straight line when graphed. It can have varying rates of change.

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CCSS.8.F.A.3

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What is the general form of a linear equation?

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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.F.A.3

CCSS.8.EE.B.6

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What does the slope of a linear function represent?

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The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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CCSS.8.EE.B.5

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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 line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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How can you determine if a function is linear from a table of values?

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If the differences between consecutive y-values are constant for equal differences in x-values, the function is linear.

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CCSS.HSF-LE.A.1B

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What is an example of a linear function?

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An example of a linear function is y = 2x + 3.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2.

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CCSS.8.F.A.3

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How do you identify a linear function from a graph?

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A linear function will graph as a straight line, while a nonlinear function will graph as a curve.

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CCSS.8.F.A.3

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What is the significance of the equation y = 8x?

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This equation represents a linear function with a slope of 8 and a y-intercept of 0.

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CCSS.8.F.A.3

CCSS.8.EE.B.6