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 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 form a straight line when graphed. Its rate of change is not constant.

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 all pairs of 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 y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

If a function has a constant slope, what type of function is it?

Back

If a function has a constant slope, it is a linear function.

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

Can a linear function have a negative slope?

Back

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

Front

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

Back

A linear function graphs as a straight line, while a quadratic function graphs as a parabola (U-shaped curve).

Front

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

Back

A function is linear if its graph is a straight line. If the graph curves, it is nonlinear.