Identifying Linear Functions

Front

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.

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

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

Back

A linear function will have a constant rate of change between the x-values and y-values. This means that the difference in y-values divided by the difference in x-values will be the same for any two points.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the equation f(x) = mx + b.

Front

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

Back

A linear function produces a straight line when graphed, while a nonlinear function produces a curve or a different shape.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-value increases, the y-value decreases.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which produces a parabolic curve when graphed.

Front

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

Back

If the graph of the function is a straight line, then the function is linear. If the graph curves, it is nonlinear.