# Lesson 14

Four Representations

Let’s contrast relationships that are and are not proportional in four different ways.

### 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.

- Write down at least four (gallons of gas, cost) pairs that fit this relationship.
- Create a graph of the relationship.
- What does 2.95 represent in this situation?
- 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.

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