Middle School Math Quiz: Y Equals Kx And Constant Of Proportionality

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Y Equals Kx And Constant Of ProportionalityQuestion 1 of 7

Two proportional relationships are given: Relationship A has the equation $y = 0.75x$ and Relationship B passes through the points $(4, 6)$ and $(8, 12)$ . Which statement is true?

Relationship A has a greater constant of proportionality than Relationship B

Relationship B has a greater constant of proportionality than Relationship A

Both relationships have the same constant of proportionality of 0.75

Both relationships have the same constant of proportionality of 1.5

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Middle School Math Quiz

Middle School Math Quiz: Y Equals Kx And Constant Of Proportionality

Practice Y Equals Kx And Constant Of Proportionality in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Y Equals Kx And Constant Of Proportionality, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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All questions

Question 1

Two proportional relationships are given: Relationship A has the equation $y = 0.75x$ and Relationship B passes through the points $(4, 6)$ and $(8, 12)$ . Which statement is true?

Relationship A has a greater constant of proportionality than Relationship B
Relationship B has a greater constant of proportionality than Relationship A (correct answer)
Both relationships have the same constant of proportionality of 0.75
Both relationships have the same constant of proportionality of 1.5

Explanation: Relationship A has

k = 0.75

. For Relationship B, using either point:

k = \frac{6}{4} = 1.5

k = \frac{12}{8} = 1.5

. Since

1.5 > 0.75

, Relationship B has the greater constant. Choice A reverses the comparison. Choice C incorrectly calculates Relationship B's constant as 0.75. Choice D correctly identifies Relationship B's constant but incorrectly states they're equal.

Question 2

A recipe calls for ingredients in proportional amounts. The relationship between cups of flour $x$ and cups of sugar $y$ is given by $y = \frac{3}{4}x$ . If a baker uses 8 cups of flour and wants to make a half-batch, how many cups of sugar should be used?

3 cups of sugar (correct answer)
4 cups of sugar
6 cups of sugar
12 cups of sugar

Explanation: For a full batch with 8 cups flour:

y = \frac{3}{4}(8) = 6

cups sugar. For a half-batch, use half of each ingredient:

\frac{8}{2} = 4

cups flour and

\frac{6}{2} = 3

cups sugar. We can verify:

y = \frac{3}{4}(4) = 3

. Choice B uses half the flour amount. Choice C uses the full-batch sugar amount. Choice D incorrectly doubles instead of halving.

Question 3

A car travels at constant speed. The equation $d = 55t$ represents the distance $d$ (in miles) traveled in $t$ hours. After traveling for some time, the car has gone 220 miles. How much farther will the car travel in the next 45 minutes?

41.25 miles (correct answer)
45 miles
55 miles
82.5 miles

Explanation: The constant of proportionality is 55 mph. Convert 45 minutes to hours:

45 \div 60 = 0.75

hours. Distance =

55 \times 0.75 = 41.25

miles. The initial 220 miles is irrelevant to the question. Choice B uses 45 without converting to hours or applying the rate. Choice C uses the speed value directly. Choice D incorrectly uses 1.5 hours instead of 0.75 hours.

Question 4

The cost of printing business cards is proportional to the number of cards printed. The relationship can be written as $C = kn$ , where $C$ is the total cost and $n$ is the number of cards. If 250 cards cost $15, what would be the cost of printing 400 cards?

$18.00
$22.50
$24.00 (correct answer)
$26.40

Explanation: First find

k

15 = k(250)

, so

k = \frac{15}{250} = 0.06

dollars per card. For 400 cards:

C = 0.06 \times 400 = 24

dollars. Choice A uses an incorrect proportion setup. Choice B uses

k = \frac{15}{400}

and multiplies by 600. Choice D uses

k = 0.066

(rounded incorrectly).

Question 5

Three students each wrote an equation to represent a proportional relationship. Alex wrote $y = 0.4x$ , Ben wrote $y = \frac{2}{5}x$ , and Carlos wrote $y = \frac{4}{10}x$ . When $x = 25$ , which student's equation gives the largest value of $y$ ?

Alex's equation gives the largest value
Ben's equation gives the largest value
Carlos's equation gives the largest value
All three equations give the same value (correct answer)

Explanation: Convert all constants to decimals: Alex has

k = 0.4

, Ben has

k = \frac{2}{5} = 0.4

, and Carlos has

k = \frac{4}{10} = 0.4

. Since all constants of proportionality are equal, when

x = 25

, all give

y = 0.4 \times 25 = 10

. Choices A, B, and C fail to recognize that the three expressions for

k

are equivalent.

Question 6

The distance a spring stretches is proportional to the weight attached to it. When 6 pounds is attached, the spring stretches 4 inches. If the spring stretches 10 inches, what weight is attached?

9 pounds
12 pounds
15 pounds (correct answer)
18 pounds

Explanation: Using

y = kx

where

y

is stretch and

x

is weight:

4 = k(6)

, so

k = \frac{4}{6} = \frac{2}{3}

. When stretch is 10 inches:

10 = \frac{2}{3}x

, so

x = 10 \times \frac{3}{2} = 15

pounds. Choice A uses incorrect proportion

\frac{6}{4} = \frac{x}{6}

. Choice B uses

\frac{6}{4} = \frac{x}{8}

. Choice D uses

\frac{6}{4} = \frac{x}{12}

Question 7

The equation $y = 2.5x$ represents the cost $y$ (in dollars) of $x$ pounds of apples. Maria buys apples and pays $12.50. She then decides to buy 2 more pounds. What is her total cost?

$17.50 (correct answer)
$15.00
$20.00
$22.50

Explanation: First, find how many pounds Maria initially bought:

12.50 = 2.5x

, so

x = 5

pounds. Then she buys 2 more pounds for a total of 7 pounds. Her total cost is

y = 2.5(7) = 17.50

dollars. Choice B incorrectly adds just the cost of 2 pounds (

2.5 \times 2 = 5

) to the original cost. Choice C uses 8 pounds instead of 7. Choice D uses 9 pounds instead of 7.