linear vs. nonlinear

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 the definition of 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

What is the general form of a linear equation?

Back

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

Front

What is the difference between linear and nonlinear graphs?

Back

Linear graphs are straight lines, indicating a constant rate of change, while nonlinear graphs can be curves, indicating a variable rate of change.

Tags

CCSS.8.F.A.3

Front

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

Back

A linear function will have a constant difference in the y-values for equal increments in the x-values.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear equation?

Back

An example of a nonlinear equation is y = x^2 or y = 1/x.

Tags

CCSS.8.F.A.3

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Tags

CCSS.8.EE.B.5

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, indicating that as x increases, y decreases.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in a linear function?

Back

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

Front

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

Back

If the graph is a straight line, the function is linear. If the graph is curved or has bends, the function is nonlinear.

Tags

CCSS.8.F.A.3