Linear vs. Nonlinear Tables and Graphs

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and 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 rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear operations.

Front

How can you identify a linear relationship in a table of values?

Back

A linear relationship in a table of values can be identified if the difference between consecutive y-values is constant for equal intervals of x-values.

Front

What does the slope of a line represent in a linear function?

Back

The slope of a line 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 line crosses the y-axis. It is the value of y when x is 0.

Front

What does it mean if a graph is nonlinear?

Back

If a graph is nonlinear, it means that the relationship between the variables does not change at a constant rate. The graph may curve or have varying slopes.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

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

Back

You can tell if a graph is linear or nonlinear by checking if the points form a straight line. If they do, it is linear; if they curve or change direction, it is nonlinear.

Front

What is the significance of a steep line in a graph?

Back

A steep line in a graph indicates a greater rate of change. The steeper the line, the more rapidly the y-value changes with respect to the x-value.

Front

What does a constant rate of change indicate in a table?

Back

A constant rate of change in a table indicates that the relationship between the x and y values is linear.