Linear vs. Nonlinear

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What is a linear function?

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A linear function is a function that graphs to a straight line. It 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

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What is a nonlinear function?

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A nonlinear function is a function that does not graph to a straight line. Its graph can be curved or have a more complex shape.

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CCSS.8.F.A.3

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How can you identify a linear function from its graph?

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A linear function can be identified by its straight line graph, which has a constant slope.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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How can you identify a nonlinear function from its graph?

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A nonlinear function can be identified by its curved or irregular graph, which does not have a constant slope.

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CCSS.8.F.A.3

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What is the slope of a linear function?

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The slope of a linear function is the rate of change of the function, represented by 'm' in the equation y = mx + b.

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CCSS.8.EE.B.5

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What does the y-intercept represent in a linear function?

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

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Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means the graph decreases as it moves from left to right.

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CCSS.8.EE.B.5

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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, which graphs as a parabola.

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CCSS.8.F.A.3

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What does it mean if a function is described as 'curved'?

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If a function is described as 'curved', it means that the graph of the function does not form a straight line and changes direction.

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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 Ax + By = C, where A, B, and C are constants.