Understanding Proportional Relationships

Mr. Weaver's lesson on proportional relationships explains how to determine if a table shows a proportional relationship by checking for a constant ratio, known as the constant of proportionality. Through examples involving granola bars, potato chips, a soccer game, and smoothie shops, the lesson illustrates how to identify proportional and non-proportional relationships. The key takeaway is that a proportional relationship maintains a consistent ratio across all instances, allowing for the creation of a linear equation.

What is a key characteristic of a proportional relationship?

• It is always greater than 1.

• It varies with each instance.

• It has an equivalent ratio every time.

• It has a constant sum.

How do you determine the constant of proportionality in the pen example?

• By subtracting the number of pens from the price.

• By multiplying the price by the number of pens.

• By adding the price and the number of pens.

• By dividing the price by the number of pens.

In the pen example, what was the constant cost per pen?

• 26 cents

• 24 cents

• 22 cents

• 20 cents

Why is the cost of chips not proportional to their size?

• The cost per ounce varies for different sizes.

• The cost per ounce is the same for all sizes.

• The total cost is always the same.

• The weight of the chips is constant.

What is the constant of proportionality for the 7.75-ounce bag of chips?

• 0.399

• 0.463

• 0.368

• 0.500

In the stadium example, what makes the relationship non-proportional?

• The ticket price decreases with more people.

• The parking fee adds a fixed amount to the total cost.

• The parking fee is variable.

• The cost per person is constant.

What would make the stadium cost proportional?

• Eliminating the parking fee.

• Adding a discount for groups.

• Increasing the parking fee.

• Reducing the ticket price.

How is Smoothie Shop A different from Smoothie Shop B?

• Shop B offers discounts on larger sizes.

• Shop A has a constant price per ounce.

• Shop B has a constant price per ounce.

• Shop A has a variable price per ounce.

What is the price per ounce for the smallest size at Smoothie Shop B?

• 70 cents

• 62.5 cents

• 67 cents

• 75 cents

Why can't we predict the price at Smoothie Shop B?

• The price per ounce is constant.

• The price per ounce varies with size.

• The shop only sells one size.

• The shop doesn't provide prices.