Identifying Linear Functions and Proportionality

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 proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant. In a graph, it is represented by a straight line that passes through the origin.

Front

What does it mean if a function is nonlinear?

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 proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin (0,0) and is straight.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and do not graph as straight lines.

Front

What does it mean for a relationship to be nonproportional?

Back

A nonproportional relationship means that the ratio between the two quantities is not constant, and the graph does not pass through the origin.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented by the value of y when x is 0.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3, which graphs as a straight line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2 - 1, which graphs as a parabola.