Proportional or Nonproportional and Constant of Proportionality

Front

What is the definition of proportional relationships?

Back

Proportional relationships are those in which two quantities maintain a constant ratio or rate. If one quantity increases, the other increases at a consistent rate.

Front

What is the constant of proportionality?

Back

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

Front

How do you calculate the average speed?

Back

Average speed is calculated by dividing the total distance traveled by the total time taken. Formula: Average Speed = Total Distance / Total Time.

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 many units of one quantity correspond to one unit of another quantity.

Front

If a 6-pack of bottled water costs $3.79, what is the cost per bottle?

Back

Cost per bottle = Total Cost / Number of Bottles = $3.79 / 6 = $0.63 per bottle.

Front

What does it mean if two quantities are nonproportional?

Back

Nonproportional quantities do not maintain a constant ratio. As one quantity changes, the other does not change at a consistent rate.

Front

How do you determine which option is the best deal when comparing prices?

Back

To determine the best deal, calculate the unit price for each option by dividing the total price by the quantity, then compare the unit prices.

Front

What is the relationship between the side length of an equilateral triangle and its perimeter?

Back

In an equilateral triangle, the perimeter is proportional to the length of one side. If the side length increases, the perimeter increases at three times that rate.

Front

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

Back

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

Front

How do you express a price of $15 for 10 gallons as a unit rate?

Back

Unit rate = Total Price / Total Gallons = $15 / 10 = $1.50 per gallon.