Linear vs NonLinear Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. It can have varying rates of change.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

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

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the function is linear.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2.

Front

How do you identify a linear function from a graph?

Back

A linear function will graph as a straight line, while a nonlinear function will graph as a curve.

Front

What is the significance of the equation y = 8x?

Back

This equation represents a linear function with a slope of 8 and a y-intercept of 0.