Proportional vs Non-Proportional

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. For example, if you double one quantity, the other quantity also doubles.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is a relationship between two quantities where the ratio is not constant. For example, if you increase one quantity, the other may increase but not at a constant rate.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship will graph as a straight line that passes through the origin (0,0).

Front

How can you identify a non-proportional relationship from a graph?

Back

A non-proportional relationship will graph as a line that does not pass through the origin or as a curve.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant ratio between two proportional quantities, often represented as 'k' in the equation y = kx.

Front

Give an example of a proportional relationship in real life.

Back

An example of a proportional relationship is the relationship between distance and time when traveling at a constant speed.

Front

Give an example of a non-proportional relationship in real life.

Back

An example of a non-proportional relationship is the relationship between the number of hours worked and the total pay when there is a base salary plus overtime pay.

Front

What is the equation for a proportional relationship?

Back

The equation for a proportional relationship is y = kx, where k is the constant of proportionality.

Front

What happens to the graph of a proportional relationship if the constant of proportionality increases?

Back

If the constant of proportionality increases, the slope of the line on the graph becomes steeper.

Front

What happens to the graph of a non-proportional relationship if one quantity increases significantly?

Back

In a non-proportional relationship, if one quantity increases significantly, the other quantity may increase but not at a constant rate, leading to a curve or a line that does not maintain a consistent slope.