linear vs. Nonlinear relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, where the rate of change is constant.

Front

What is a nonlinear relationship?

Back

A nonlinear relationship is a relationship between two variables that cannot be represented by a straight line on a graph, where the rate of change varies.

Front

How can you determine if a table represents a linear relationship?

Back

You can determine if a table represents a linear relationship by checking if the rate of change (slope) between the x and y values is constant.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change between the dependent variable (y) and the independent variable (x).

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

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, which produces a parabolic graph.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x) has exactly one output (y). A relation can have multiple outputs for a single input.

Front

What is a common characteristic of linear functions in terms of their graph?

Back

Linear functions graph as straight lines, and they have a constant slope.

Front

What is a common characteristic of nonlinear functions in terms of their graph?

Back

Nonlinear functions graph as curves or shapes that are not straight lines, indicating varying rates of change.

Front

How can you identify a nonlinear function from a graph?

Back

You can identify a nonlinear function from a graph by looking for curves or bends, rather than a straight line.