Constant of proportionality and Unit Rate

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities. It can be found by dividing one quantity by the other.

Front

How do you write an equation for a proportional relationship?

Back

An equation for a proportional relationship can be written in the form y = kx, where k is the constant of proportionality.

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 the unit rate from a given distance and time?

Back

To calculate the unit rate, divide the total distance by the total time. For example, if Josie runs 2 1/4 miles in 3/4 hour, her unit rate is 2.25 miles / 0.75 hours = 3 miles per hour.

Front

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

Back

To find the constant of proportionality (k) from a table, divide the value of y by the corresponding value of x for any pair of values.

Front

If a faucet leaks 5/8 quart in 15 minutes, how do you find the leak rate per hour?

Back

To find the leak rate per hour, first find the rate per minute (5/8 quart / 15 minutes), then multiply by 60 minutes to get the rate per hour.

Front

What is the better buy: a 12-pack of soda for $3.50 or a 6-pack for $1.80?

Back

To determine the better buy, calculate the unit price for each option. The 12-pack costs $0.2917 per can, while the 6-pack costs $0.30 per can. The 12-pack is the better buy.

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 identify if a relationship is proportional from a graph?

Back

A relationship is proportional if the graph is a straight line that passes through the origin (0,0).

Front

What is the relationship between unit rate and constant of proportionality?

Back

The unit rate is the constant of proportionality expressed in terms of one unit of the second quantity. It shows how much of one quantity corresponds to one unit of another.