Proportional Relationships and Rates

The video tutorial explains proportional relationships, focusing on the constant of proportionality. It provides examples, such as calculating the cost per ticket and the cost of apples, to illustrate how to set up and solve equations. The tutorial also applies these concepts to real-world scenarios like fuel consumption and travel distance. Additionally, it analyzes a graph to understand proportional relationships in art, specifically in Andrea's portrait drawing. The video emphasizes the importance of the constant of proportionality in writing equations and solving problems.

What is the constant of proportionality in a proportional relationship?

• The sum of all ratios

• The difference between two variables

• The constant ratio or unit rate

• The product of two variables

How do you write an equation for a proportional relationship?

• By dividing the variables

• By subtracting the variables

• By setting up a proportion and cross-multiplying

• By adding the variables

If the total cost of movie tickets is $28 for 3 friends, what is the cost per ticket?

• $7.00

• $8.50

• $9.00

• $9.33

What equation represents the cost of apples if 4 apples cost $5?

• y = 5x

• y = 1.50x

• y = 4x

• y = 1.25x

How many miles can a car travel on one gallon of gas if the constant of proportionality is 28?

• 14 miles

• 28 miles

• 7 miles

• 56 miles

Will a car with half a gallon of gas reach a gas station 26 miles away if it travels 28 miles per gallon?

• It depends on the weather

• No, it will not reach

• Yes, it will reach

• It depends on the speed

How far can a car travel on 18 gallons of gas if the constant of proportionality is 28?

• 504 miles

• 400 miles

• 450 miles

• 550 miles

How many gallons of gas are needed to travel 750 miles if the car travels 28 miles per gallon?

• 26.79 gallons

• 25 gallons

• 28 gallons

• 30 gallons

What does the ordered pair (2, 3) represent in the context of the artist's portraits?

• 2 portraits in 3 hours

• 3 portraits in 2 hours

• 2 hours for 3 portraits

• 3 hours for 2 portraits

What is the constant of proportionality for the artist's portraits if she draws 1.5 portraits per hour?

• 1.5

• 2.0

• 3.0

• 1.0