Linear vs. Nonlinear Tables and Graphs

Front

What is the difference between linear and nonlinear relationships?

Back

Linear relationships have a constant rate of change and can be represented by a straight line, while nonlinear relationships do not have a constant rate of change and can be represented by curves.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

Front

What does a steep line on a graph indicate about the rate of change?

Back

A steep line indicates a higher rate of change.

Front

What is the definition of a rate of change in a function?

Back

The rate of change is the ratio of the change in the dependent variable to the change in the independent variable.

Front

What are initial values in the context of functions?

Back

Initial values refer to the starting point of a function, often represented as the y-intercept in a graph.

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 change in the output value is consistent for equal changes in the input value.

Front

How can you determine if a graph is nonlinear?

Back

A graph is nonlinear if it curves or does not form a straight line.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function and the direction of the relationship between the variables.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is a quadratic function, such as y = x^2.

Front

How do you find the slope of a line on a graph?

Back

The slope can be found by selecting two points on the line and using the formula (change in y) / (change in x).