Constant of Proportionality

Front

What is the constant of proportionality?

Back

The constant of proportionality is a constant ratio or unit rate that describes how one quantity changes in relation to another. It is often represented by the letter 'k'.

Front

How do you find the unit rate?

Back

To find the unit rate, divide the total quantity by the number of units. For example, if a box of cereal costs $3.59 for 30 oz, the unit rate is $3.59 ÷ 30 oz = $0.1197, which rounds to 12 cents per ounce.

Front

What does it mean if two quantities are proportional?

Back

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

Front

If k = 6, what does this represent in a proportional relationship?

Back

If k = 6, it means that for every unit of the first quantity, the second quantity is 6 times that amount. This is the constant of proportionality.

Front

What is the unit rate of 624 calories in 3 servings?

Back

The unit rate is 624 calories ÷ 3 servings = 208 calories per serving.

Front

In the recipe, if 3/4 cup of brown sugar is used for 3 eggs, what is the unit rate of eggs per cup?

Back

The unit rate is 3 eggs ÷ (3/4 cup) = 4 eggs per cup.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities increase or decrease at the same rate, resulting in a constant ratio.

Front

How can you determine if a relationship is proportional from a table of values?

Back

A relationship is proportional if the ratios of corresponding values are constant. For example, if you have a table of values and the ratio of y to x is the same for all pairs, then the relationship is proportional.

Front

What is the formula for finding the constant of proportionality?

Back

The formula for finding the constant of proportionality (k) is k = y/x, where y is the dependent variable and x is the independent variable.

Front

If a car travels 120 miles in 2 hours, what is the constant of proportionality for speed?

Back

The constant of proportionality for speed is 120 miles ÷ 2 hours = 60 miles per hour.