Linear vs Non-linear

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What is a linear function?

Back

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.

Tags

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 graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

Tags

CCSS.8.F.A.3

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How can you tell if a graph represents a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function. If a vertical line crosses the graph more than once, it is not a function.

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it forms a straight line, indicating a constant rate of change between the variables.

Tags

CCSS.8.F.A.3

Front

What does it mean for a graph to be nonlinear?

Back

A graph is nonlinear if it does not form a straight line, indicating that the rate of change between the variables is not constant.

Tags

CCSS.8.F.A.3

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3, which graphs to a straight line.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2, which graphs to a parabola.

Tags

CCSS.8.F.A.3

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.