Understanding Proportional Relationships

The lesson covers comparing relationships using tables, focusing on scale factors, cost calculations, and proportionality. It includes practical examples like adjusting a lemonade recipe, calculating state park entry costs, and analyzing running paces. The lesson concludes with a summary and homework on identifying proportional relationships.

If you want to double the amount of lemonade while keeping the taste the same, what should you do?

• Add more water only

• Use a scale factor of 2 for all ingredients

• Add more lemons only

• Use a scale factor of 0.5 for all ingredients

What happens to the cost per person when more people are added to a vehicle entering the state park?

• It decreases

• It stays the same

• It doubles

• It increases

How can you determine if a runner is maintaining a constant pace?

• By observing the runner's speed visually

• By measuring the distance covered

• By comparing the runner's start and end times

• By checking if the time per lap is the same

What is a key indicator of a proportional relationship?

• The presence of a constant quotient

• The presence of a constant product

• The presence of a constant difference

• The presence of a constant sum

In the taxi fare example, why is the relationship not proportional?

• Because the fare decreases with distance

• Because there is an initial fixed cost

• Because the fare is constant regardless of distance

• Because the fare increases with distance

What is the effect of doubling both the length and width of a rectangular field on the diagonal?

• The diagonal remains the same

• The diagonal doubles

• The diagonal triples

• The diagonal halves

How do you find the constant of proportionality in a table?

• By dividing y by x

• By subtracting the x values from y values

• By adding the x and y values

• By multiplying x and y

In the race between the turtle and the rabbit, which one is running at a proportional rate?

• The turtle

• The rabbit

• Both

• Neither

What happens to the cost per ounce of a drink as the size increases?

• It decreases

• It doubles

• It increases

• It stays the same

What is the formula for a proportional relationship?

• y = x + k

• y = kx

• y = mx + b

• y = k + x