Comparing Relationships with Tables

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Do all Plane Figures Tile a Plane?

(A). Entrance to a state park costs $6 per vehicle, plus $2 per person in the vehicle. Complete the table and answer the questions below.

(1). For each row in the table, if each person in the vehicle splits the entrance cost equally, how much will each person pay?

(2). How might you determine the entrance cost for a bus with 50 people?

(3). Is the relationship between the number of people and the total entrance cost a proportional relationship? Explain how you know.

(4). What equation could you use to find the total entrance cost for a vehicle with any number of people?

(B). A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey. Invent four new versions of this lemonade recipe:

(1). One that would make more lemonade but taste the same as the original recipe.

(2). One that would make less lemonade but taste the same as the original recipe.

(3). One that would have a stronger lemon taste than the original recipe.

(4). One that would have a weaker lemon taste than the original recipe.

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Comparing Relationships in a Table of Proportional Relationships.

Han and Clare were running laps around the track. The coach recorded their times at the end of laps 2, 4, 6, and 8. Complete the table of Han’s run.

(1). Now complete the table of Clare’s run and answer the questions below.

(2). Is Han running at a constant pace? How do you know?

(3). Is Clare running at a constant pace? How do you know?

(4). Write an equation for the relationship between distance and time for anyone who is running at a constant pace.

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Finding the Constant of ProportFrom a Table.

Study the values in the following tables of proportional relationships and answer the question that follows.

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A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional for either one? If so, write an equation that represents the relationship.

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A taxi service charges $1.00 for the first mile, then $0.10 for each additional mile after that. Fill in the table with the missing information and answer the question below.