Linear vs. Nonlinear

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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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. Its rate of change varies, and it can be represented by equations that include exponents, roots, or other non-linear terms.

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CCSS.8.F.A.3

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How can you identify a linear equation?

Back

A linear equation can be identified by its standard form, which is Ax + By = C, where A, B, and C are constants. It can also be recognized if it can be rearranged into the form y = mx + b.

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What does the graph of a linear function look like?

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The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the graph of a nonlinear function look like?

Back

The graph of a nonlinear function can take various shapes, such as curves, parabolas, or circles, and does not form a straight line.

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CCSS.8.F.A.1

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Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation y = mx + b. 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 in a linear function?

Back

The y-intercept is the point where the graph of a linear function crosses the y-axis. It is represented by 'b' in the equation y = mx + b.

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Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line and does not change in the y-value as x changes.

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CCSS.8.EE.B.5

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What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3, which has a slope of 2 and a y-intercept of 3.

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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 and does not form a straight line.

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CCSS.8.F.A.3