Proportional or Not

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio to each other. This means that as one quantity increases or decreases, the other quantity does so in a consistent manner.

Front

How can you identify if a relationship is proportional?

Back

A relationship is proportional if the ratio of the two quantities is constant. You can check this by dividing one quantity by the other; if the result is the same for all pairs of values, the relationship is proportional.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship occurs when the ratio between two quantities changes. This means that as one quantity changes, the other does not change in a consistent way.

Front

Give an example of a proportional relationship.

Back

An example of a proportional relationship is the relationship between distance and time when traveling at a constant speed. If you travel at 60 miles per hour, the distance traveled is proportional to the time spent traveling.

Front

Give an example of a non-proportional relationship.

Back

An example of a non-proportional relationship is the relationship between the number of hours worked and the total pay if the pay rate changes after a certain number of hours.

Front

What is the formula for finding the constant of proportionality?

Back

The constant of proportionality can be found using the formula k = y/x, where k is the constant, y is the dependent variable, and x is the independent variable.

Front

What is a graph of a proportional relationship like?

Back

A graph of a proportional relationship is a straight line that passes through the origin (0,0). The slope of the line represents the constant of proportionality.

Front

What is a graph of a non-proportional relationship like?

Back

A graph of a non-proportional relationship may be a curve or a line that does not pass through the origin. The slope of the line may change at different points.

Front

What is the difference between direct and inverse proportionality?

Back

Direct proportionality means that as one quantity increases, the other also increases. Inverse proportionality means that as one quantity increases, the other decreases.

Front

How do you solve a problem involving proportional relationships?

Back

To solve a problem involving proportional relationships, set up a proportion (a fraction equal to another fraction) and cross-multiply to find the unknown value.