Constant of Proportionality

Front

What is the constant of proportionality?

Back

The constant of proportionality is a constant value that relates two proportional quantities, often represented as 'k' in the equation y = kx.

Front

How do you find the constant of proportionality from a ratio?

Back

To find the constant of proportionality, divide one quantity by the other in the ratio. For example, if the ratio is 3:1, the constant of proportionality is 3.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity.

Front

How do you calculate a unit rate?

Back

To calculate a unit rate, divide the quantity of interest by the number of units. For example, if you have 60 miles in 2 hours, the unit rate is 60 miles ÷ 2 hours = 30 miles per hour.

Front

What is the unit rate of 240 calories in 4 servings?

Back

The unit rate is 240 calories ÷ 4 servings = 60 calories per serving.

Front

If a car travels 180 miles in 3 hours, what is the constant of proportionality in miles per hour?

Back

The constant of proportionality is 180 miles ÷ 3 hours = 60 miles per hour.

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, meaning as one quantity increases, the other quantity increases at a consistent rate.

Front

How can you represent a proportional relationship graphically?

Back

A proportional relationship can be represented graphically by a straight line that passes through the origin (0,0) on a coordinate plane.

Front

What is the formula for finding the constant of proportionality in a direct variation problem?

Back

The formula is y = kx, where 'k' is the constant of proportionality, 'y' is the dependent variable, and 'x' is the independent variable.

Front

If a recipe requires 2 cups of flour for every 3 cups of sugar, what is the constant of proportionality for flour to sugar?

Back

The constant of proportionality is 2/3, meaning for every 2 cups of flour, there are 3 cups of sugar.