Linear vs Nonlinear

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What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. The rate of change is constant.

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CCSS.HSF-LE.A.1B

Front

What is a nonlinear relationship?

Back

A nonlinear relationship is a relationship between two variables that does not form a straight line when graphed. The rate of change is not constant.

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CCSS.8.F.A.3

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

Back

A linear function will have a constant rate of change between the x and y values.

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CCSS.HSF-LE.A.1B

Front

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

Back

A nonlinear function will have a varying rate of change between the x and y values.

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CCSS.HSF-LE.A.1B

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What does it mean for a function to have a constant rate of change?

Back

It means that for every unit increase in the x value, the y value increases by a fixed amount.

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CCSS.HSF-LE.A.1B

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What does it mean for a function to have a variable rate of change?

Back

It means that the amount by which the y value increases for each unit increase in the x value changes.

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CCSS.HSF-LE.A.1B

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Give an example of a linear relationship in real life.

Back

An example is the cost of tickets for a concert where each ticket costs the same amount.

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CCSS.HSF-LE.A.1B

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Give an example of a nonlinear relationship in real life.

Back

An example is the relationship between the area of a circle and its radius, where the area increases with the square of the radius.

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CCSS.8.F.A.3

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What is the slope of a linear function?

Back

The slope is the ratio of the change in the y value to the change in the x value, indicating the steepness of the line.

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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 line crosses the y-axis, representing the value of y when x is zero.