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 the form f(x) = 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 form a straight line when graphed. Its graph can be curved or have varying slopes.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear equation from a set of equations?

Back

A linear equation will have variables raised only to the first power and can be written in the form Ax + By = C.

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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 its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

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

Back

The y-intercept is the point where the graph of the equation crosses the y-axis, representing the value of y when x is zero.

Front

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.

Tags

CCSS.8.EE.B.5

Front

What is the general form of a linear equation in two variables?

Back

The general form of a linear equation in two variables is Ax + By + C = 0, where A, B, and C are constants.

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have bends, indicating a change in direction.

Tags

CCSS.8.F.A.3

Front

What is a common example of a nonlinear function?

Back

A common example of a nonlinear function is a quadratic function, such as f(x) = ax^2 + bx + c.

Tags

CCSS.8.F.A.3

Front

How do you determine if a graph is linear or nonlinear?

Back

To determine if a graph is linear or nonlinear, check if it forms a straight line. If it curves or has varying slopes, it is nonlinear.

Tags

CCSS.8.F.A.3