Linear vs. Nonlinear Tables and Graphs

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and 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 create a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Tags

CCSS.8.F.A.3

Front

How can you determine if a table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values (the rate of change) are constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a line represent in a linear function?

Back

The slope of a line represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

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 line crosses the y-axis. It represents the value of y when x is zero.

Front

What is the general form of a linear equation?

Back

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

Front

How can you identify a nonlinear graph?

Back

A nonlinear graph can be identified by its curved shape, which indicates that the rate of change is not constant.

Tags

CCSS.8.F.A.3

Front

What is the difference between a steep and a gentle slope?

Back

A steep slope indicates a large change in y for a small change in x, while a gentle slope indicates a small change in y for a larger change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

A function has a constant rate of change if the change in the output (y) is proportional to the change in the input (x) across the entire domain.

Tags

CCSS.HSF-LE.A.1B

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is a quadratic function, such as y = x^2, which produces a parabolic graph.

Tags

CCSS.8.F.A.3