LInear vs Nonlinear

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Its graph can be curved or have varying slopes.

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept (b) is the point where the graph of the function crosses the y-axis. It represents the value of y when x is 0.

Front

How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation being in the form y = mx + b or y = mx, where m and b are constants.

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 an example of a linear function?

Back

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

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2 or y = sin(x).

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 difference in y-values divided by the difference in x-values is the same for any two points on the line.

Front

How can you tell if a graph is linear or nonlinear?

Back

A graph is linear if it forms a straight line. It is nonlinear if it curves or has bends.