# Lesson 14

Four Representations

The practice problem answers are available at one of our IM Certified Partners

### Problem 1

The equation $$c = 2.95g$$ shows how much it costs to buy gas at a gas station on a certain day. In the equation, $$c$$ represents the cost in dollars, and $$g$$ represents how many gallons of gas were purchased.

1. Write down at least four (gallons of gas, cost) pairs that fit this relationship.
2. Create a graph of the relationship.
3. What does 2.95 represent in this situation?
4. Jada’s mom remarks, “You can get about a third of a gallon of gas for a dollar.” Is she correct? How did she come up with that?

### Problem 2

There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons, as shown in the graph.

1. Plot and label at least two more points that represent the relationship.
2. Use a straightedge to draw a line that represents this proportional relationship.
3. For which value y is ($$1, y$$) on the line you just drew?
4. What is the constant of proportionality for this relationship?
5. Write an equation representing this relationship. Use $$c$$ for cups and $$t$$ for tablespoons.