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Constant of Proportionality

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Constant of Proportionality

For each proportional relationship, identify the constant of proportionality. Show calculations where asked. Use the units given in each question.

Recognize the constant

Use ratios and equations to identify proportional relationships.

Pints of berries

Total cost ($)

3.50

7.00

17.50

1.According to the berry-price table, what is the constant of proportionality in dollars per pint?

$1.75 per pint
$3.50 per pint
$7.00 per pint
$17.50 per pint

2.Which situation describes a proportional relationship?

Andre earns $18 for every hour he works, with no starting bonus.
The temperature changes throughout the afternoon.
Carlos’s height compared with his age.
A market’s daily number of customers.

3.Madison uses 5 cups of oats to make 20 servings of a snack mix. What is the constant of proportionality in cups of oats per serving?

0.25 cup per serving
4 cups per serving
5 cups per serving
15 cups per serving

4.Select the combination of valid ways to find the constant of proportionality k in a relationship written as y = kx.

Divide y by x for a corresponding pair of values; read the coefficient of x in y = kx; find the slope of the proportional relationship’s line through the origin.
Divide y by x for a corresponding pair of values; add x and y for one pair and call the sum k.
Read the coefficient of x in y = kx; add x and y for one pair and call the sum k.
Find the slope of the proportional relationship’s line through the origin; add x and y for one pair and call the sum k.

5.A vendor sells 4 bags of apples for $10. What is the constant of proportionality in dollars per bag?

Calculate and explain

Use tables, equations, and unit rates to solve each problem.

6.A proportional relationship pairs 3 hours of work with $42 earned. Calculate the earnings for 5 and 8 hours, then state the constant of proportionality in dollars per hour.

7.The equation y = 9x represents a proportional relationship. Identify its constant of proportionality. Then find y when x = 6.

8.A delivery van travels 156 miles using 6 gallons of fuel. Find the constant of proportionality in miles per gallon. Show the division you used.

9.Explain what the constant of proportionality means in the equation y = 4.5x. Include what happens to y for each increase of 1 in x.

10.Match each proportional equation to its constant of proportionality.

y = 12x
y = 0.4x
y = 2.5x
y = 7x

Apply proportional reasoning

Use the constant to write equations and solve real-world problems.

11.At a farmers’ market, a vendor charges $2.25 for each jar of honey. Write an equation for total cost C in terms of the number of jars j. Then find the cost of 8 jars.

12.At a produce stand, 3 pounds of peaches cost $7.50. If the price stays proportional, what will 11 pounds cost?