Four Representations

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Finding Pairs that Satisfy a Proportional Relationship.

The equation  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. 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 below.

(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?

(5). How did she come up with that?

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Writing an Equation for a Proportional Relationship.

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.

On the graph above:

(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 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.

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Adding More Points on a Graph of Proportional Relationship.

(A). 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

(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?

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A gas station charges four different prices for gas: a day price, a night price, a weekend price, and a weekend night price. Each price is represented in a different way:

(1). What are the similarities and the differences among the different representations?

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Which group of blocks is the bluest? Explain your reason.

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Order the groups of blocks from least blue to bluest.