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.

  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.
Graph of a point on coordinate plane, origin O. Horizontal axis, volume in cups, scale 0 to 6, by 1’s. Vertical axis, volume in tablespoons, scale 0 to 70, by 10’s. Point at (3 comma 48).