Proportional Relationships and Rates

This video tutorial by Mr. Holcomb covers lesson 8 on representing proportional relationships with equations. It explains the concept of proportional relationships, unit rates, and the constant of proportionality. The video demonstrates how to write and rearrange equations using inverse operations and provides examples, such as calculating gas mileage and Andrea's portraits, to illustrate these concepts. The lesson concludes with a summary of key points.

What is the constant of proportionality in a proportional relationship?

• The product of y and x

• The ratio of y to x

• The difference between y and x

• The sum of all x-values

Which operation is the inverse of multiplication?

• Division

• Subtraction

• Addition

• Exponentiation

If K equals Y divided by X, how can you solve for Y?

• Divide both sides by K

• Add X to both sides

• Subtract K from both sides

• Multiply both sides by X

In the gas consumption example, what does a constant of proportionality of 28 represent?

• 28 gallons per mile

• 28 miles per gallon

• 28 miles per hour

• 28 gallons per hour

How far can the car travel on half a gallon of gas?

• 28 miles

• 26 miles

• 12 miles

• 14 miles

What is the equation used to determine the distance traveled based on gallons of gas?

• G = M/28

• M = G/28

• G = 28M

• M = 28G

In Andrea's portraits example, what does the constant of proportionality of 3/2 mean?

• 3 portraits in 1 hour

• 2 portraits in 3 hours

• 2 portraits in 1 hour

• 3 portraits in 2 hours

How many portraits can Andrea draw in 6 hours?

• 9 portraits

• 6 portraits

• 3 portraits

• 12 portraits

What is the unit rate of portraits per hour for Andrea?

• 2 portraits per hour

• 1.5 portraits per hour

• 1 portrait per hour

• 3 portraits per hour

Which equation represents the relationship between time and portraits drawn?

• T = 3/2 N

• N = 2/3 T

• N = 3/2 T

• T = 2/3 N