Linear vs Non-linear

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. It may have curves or bends.

Front

What does it mean for a function to have a constant rate of change?

Back

A constant rate of change means that for every unit increase in the input (x), the output (y) increases by a fixed amount.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope in a linear function?

Back

The slope is a measure of how steep the line is. It represents the rate of change of y with respect to x.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the coordinates (0, b).

Front

How can you tell if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is an example of a linear relationship in real life?

Back

An example of a linear relationship is the cost of a meal that has a fixed delivery fee plus a cost per person.

Front

What is an example of a non-linear relationship in real life?

Back

An example of a non-linear relationship is the path of a thrown ball, which follows a curved trajectory.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases.