Constant of Proportionality Practice

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented as 'k'. It remains constant for all pairs of values in a proportional relationship.

Front

How do you find the constant of proportionality from a given total and number of servings?

Back

Divide the total amount by the number of servings. For example, if there are 624 calories in 3 servings, the constant of proportionality is 624 ÷ 3 = 208 calories per serving.

Front

What does it mean if a relationship is proportional?

Back

A relationship is proportional if the ratio between two quantities is constant. This means that as one quantity increases or decreases, the other does so in a consistent manner.

Front

If Craig earns $37 for 4 hours, what is his hourly rate?

Back

To find the hourly rate, divide the total earnings by the number of hours: $37 ÷ 4 = $9.25 per hour.

Front

What is the constant of proportionality in the equation y = kx?

Back

In the equation y = kx, 'k' represents the constant of proportionality, which indicates how much y changes for a unit change in x.

Front

If a table shows values (2, 6), (4, 12), and (6, 18), is this a proportional relationship?

Back

Yes, this is a proportional relationship because the ratio of y to x is constant (3 in this case).

Front

What is the formula to calculate the constant of proportionality from a table of values?

Back

The constant of proportionality can be calculated by dividing the y-value by the corresponding x-value for any pair of values in the table.

Front

If k = 5, what does this mean in a proportional relationship?

Back

This means that for every unit increase in x, y increases by 5 units, indicating a direct proportionality.

Front

How can you determine if a relationship is not proportional?

Back

A relationship is not proportional if the ratios of corresponding values are not constant. For example, if the ratio changes with different pairs of values.

Front

What is the constant of proportionality if a recipe requires 3 cups of flour for 12 cookies?

Back

The constant of proportionality is 3 cups ÷ 12 cookies = 0.25 cups of flour per cookie.