Proportional Relationships Quiz

Determine whether two quantities have a proportional relationship by examining a table, graph or written description. Two quantities x and y have a proportional relationship if all the ratios x/y for related pairs of x and y are equivalent. A proportion is an equation that states that two ratios are equal. Which of the following sets of ratios shows a proportional relationship?

• 3/120 and 6/240

• 4/100 and 10/250

• 5/150 and 10/300

• 7/210 and 14/420

Answer explanation

The set of ratios 5/150 and 10/300 shows a proportional relationship because they are equivalent ratios, indicating a proportional relationship between the quantities.

Angela is training for a marathon and completes her long mileage runs for training on the weekend. Over the last 3 weekends she ran 15 miles in 2 hours; 18 miles in 2 hours, 33 minutes; and 22 miles in 3 hours, 7 minutes. Determine if her weekend training runs showcase a proportional relationship.

• Yes, because the ratios of miles to hours are equivalent.

• No, because the ratios of miles to hours are not equivalent.

• Yes, because the total miles run is increasing each weekend.

• No, because the time taken to run is not the same each weekend.

Answer explanation

No, because the ratios of miles to hours are not equivalent.

After a workout at the gym, three friends made protein shakes to help in their recovery. Each protein shake contains 2 scoops of protein powder and 12 ounces of water. What is the constant of proportionality for this relationship?

• 2 scoops per 6 ounces of water

• 6 scoops per 12 ounces of water

• 1 scoop per 6 ounces of water

• 1 scoop per 12 ounces of water

Answer explanation

The constant of proportionality is 1 scoop per 6 ounces of water because each shake contains 2 scoops of protein powder and 12 ounces of water, which simplifies to 1 scoop per 6 ounces of water.

Determine the constant of proportionality for the following proportional relationships.

What does the graph of a proportional relationship look like?

• A) A curved line through the origin

• B) A straight line through the origin

• C) A straight line that does not pass through the origin

• D) A series of disconnected points

Answer explanation

A proportional relationship is represented by a straight line passing through the origin, showing that the two variables are directly proportional to each other.

In the context of the graph provided, what does the point (x, y) represent?

• A) The total number of tickets

• B) The cost of one ticket

• C) The total cost of x tickets

• D) The number of tickets left

Answer explanation

The point (x, y) on the graph represents the total cost of x tickets, making option C the correct choice.

According to the graph, how much does one ticket cost?

• A) $2.10

• B) $5.00

• C) $10.00

• D) $1.00

Answer explanation

According to the graph, one ticket costs $1.00, which corresponds to option D.

What is the equation that represents the proportional relationship between the number of Hass avocados purchased and the total cost?

• A) c = 2.10a

• B) c = a/2.10

• C) a = c/2.10

• D) a = 2.10c

Answer explanation

Answer Explanation highlighting the correct choice A) c = 2.10a

What is the constant of proportionality, k, in the equation y = kx?

• A) The total cost

• B) The number of items

• C) The value that relates x and y

• D) The difference between x and y

Answer explanation

The constant of proportionality, k, in the equation y = kx is the value that relates x and y.

Based on the table provided, what is the value of y when x = 5?

• A) 5

• B) 10

• C) 25/2

• D) 5/2

Answer explanation

When x = 5, y = 5^2 = 25. Therefore, the value of y when x = 5 is 25/2.