Linear Functions: Tables and Graphs

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form 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 in 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 y = mx + b.

Front

How can you determine if a graph is linear?

Back

A graph is linear if it forms a straight line. If the graph curves or has any bends, it is not linear.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its rate of change varies and can include curves, parabolas, and other shapes.

Front

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

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph to straight lines, while nonlinear functions have varying rates of change and graph to curves.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases. This is represented by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases. This is represented by a negative slope.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).