Proportional Relationships and Scale Factors

The video tutorial covers comparing relationships using tables, focusing on scale factors, cost analysis, and proportionality. It includes practical examples like adjusting a lemonade recipe, calculating costs at a state park, and analyzing running paces. The tutorial concludes with a summary and homework instructions.

What is the main focus of the lesson on comparing relationships with tables?

• Understanding geometric shapes

• Studying chemical reactions

• Exploring scale factors and rates

• Learning about historical events

If a recipe calls for 5 lemons, 2 cups of water, and 2 tablespoons of honey, what would be the new quantities if you apply a scale factor of 2?

• 10 lemons, 4 cups of water, 4 tablespoons of honey

• 8 lemons, 3 cups of water, 3 tablespoons of honey

• 5 lemons, 2 cups of water, 2 tablespoons of honey

• 2.5 lemons, 1 cup of water, 1 tablespoon of honey

How does adding more people to a vehicle affect the cost per person at the state park?

• Keeps the cost per person the same

• Decreases the cost per person

• Increases the cost per person

• Doubles the cost per person

What equation represents the total cost for a vehicle with any number of people at the state park?

• C = 2P + 6

• C = 6P + 2

• C = P + 6

• C = 2P

In the running laps activity, what indicates that Han is not running at a constant pace?

• He runs faster than CLA

• He finishes all laps in the same time

• His constant proportionality changes

• His time per lap remains the same

What is the constant proportionality for CLA's running pace?

• 1.5

• 2.0

• 3.0

• 2.5

What is a key indicator of a proportional relationship in the smoothie shop example?

• The price per ounce changes with size

• The price per ounce remains constant

• The total price is the same for all sizes

• The size of the smoothie is irrelevant

In the homework section, what is a sign that a relationship is not proportional?

• The quotient of y/x is constant

• The quotient of y/x varies

• The equation can be written as y = kx

• The relationship is linear