Practice Topic 2 Assessment

The equation y = 7.6x represents a proportional relationship. What is the constant of proportionality?

• 7.6

• x

• y

Answer explanation

The equation y = 7.6x represents a proportional relationship. To find the constant of proportionality, we look for the value that relates the change in y to the change in x. In this case, the constant of proportionality is 7.6, which means that for every unit increase in x, y increases by 7.6 units. Therefore, the correct choice is 7.6.

The tables show the numbers of green and purple beads Mia and Riley used to make 5 different decorative picture frames.

Part A:

Are the numbers of green and purple beads in Mia’s picture frames proportional? Write an equation that relates the number of purple beads, p, to the number of green beads, g.

Part B:

Are the numbers of green and purple beads in Riley’s picture frames proportional? Write an equation that relates the number of purple beads, p, to the number of green beads, g.

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The graph shows how many sheets of paper a paper-folding machine can fold in a certain number of minutes.

Part A:

What is the constant of proportionality, and what does it mean in this situation?

Part B:

Choose one ordered pair on the graph. What does it represent in this situation?

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Answer explanation

Part A: 150; The machine folds 150 sheets in 1 minute.

Part B: (40, 6,000); the machine folds 6,000 sheets in 40 minutes.

• 4 miles per hour

Answer explanation

Janet hiked a distance of 3/8 mile in 1/4 hour. To find her speed in miles per hour, we divide the distance by the time. Therefore, she hiked at a speed of 1 1/2 miles per hour. This is the correct choice as it matches the given answer.

Rachel used 4.5 cups of apple juice in a holiday fruit punch that serves 12 people. Art used 4.75 cups of apple juice in a holiday fruit punch that serves 10 people. How much more apple juice is in one serving of Art’s holiday fruit punch?

• 0.05 cup

• 0.1 cup

• 0.375 cup

• 0.475 cup

Answer explanation

To find out how much more apple juice is in one serving of Art's holiday fruit punch, we need to calculate the difference in the amount of apple juice used by Rachel and Art. Rachel used 4.5 cups for 12 people, which means each serving contains 4.5/12 = 0.375 cups. Art used 4.75 cups for 10 people, so each serving contains 4.75/10 = 0.475 cups. The difference between the two is 0.475 - 0.375 = 0.1 cup. Therefore, there is 0.1 cup more apple juice in one serving of Art's holiday fruit punch.

The water pump for a swimming pool can move 166.5 gallons of water in 3 minutes. The number of gallons, g, is proportional to the number of minutes, m, that the pump operates. Which of the following equations represents the relationship between g and m? Select all that apply.

• g = 55.5m

• g=0.02m

• m = 55.5g

Answer explanation

The question asks for the equation that represents the relationship between the number of gallons, g, and the number of minutes, m, that the water pump operates. The correct equation is g = 55.5m, which means that the number of gallons is proportional to the number of minutes. This equation is derived from the given information that the water pump can move 166.5 gallons of water in 3 minutes. Therefore, the correct choice is g = 55.5m.

Mathematical Equivalence

ON

At the local bookstore, Jim bought 2 paperback books for $13.00. Maria bought 5 paperback books for $32.50. Tanya bought 7 paperback books for $45.50.

Part A:

Do the number of books and the cost have a proportional relationship? Explain.

Part B:
What does the point (1, 6.50) represent in this situation? What does the point (0, 0) represent?

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Answer explanation

Part A: Yes; Sample answer: The graph is a line that passes through the origin.

Part B: 1 paperback book costs $6.50; no paperback books cost $0.