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Quizzes > High School Quizzes > Mathematics

Constant of Proportionality Practice Quiz

Sharpen your proportional reasoning with guided practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a Proportionality Power-Up trivia quiz for middle school math skills.

If y is directly proportional to x and y = 12 when x = 3, what is the constant of proportionality?
4
9
12
3
The constant of proportionality (k) is found by dividing y by x, so k = 12 ÷ 3 = 4. This value maintains the proportional relationship between y and x.
A table shows that when x = 2, y = 10 in a proportional relationship. What is y when x = 5?
35
20
30
25
The constant k is 10 ÷ 2 = 5. Multiplying the constant by x = 5 gives y = 5 × 5 = 25, which maintains the proportional ratio.
In a direct proportional relationship, if x doubles, what happens to y?
y halves
y stays the same
y doubles
y increases by 10
Since y and x are directly proportional, doubling the value of x doubles y as well. The constant of proportionality remains unchanged, ensuring that the relationship holds.
If 8 is to y as 4 is to 10 in a proportion, what is the value of y?
24
16
12
20
By setting up the proportion 8/y = 4/10 and cross multiplying, we obtain 8 × 10 = 4 × y. Solving for y gives y = 20, maintaining the constant ratio.
If a recipe requires 3 cups of flour for 4 servings, how many cups of flour are needed for 8 servings?
8
6
7
5
The ratio of flour to servings is 3 cups for 4 servings, which is 0.75 cups per serving. For 8 servings, multiply 0.75 by 8 to get 6 cups.
The equation y = kx represents a proportional relationship. If y = 15 when x = 5, what is k and what is y when x = 7?
k = 3, y = 24
k = 2.5, y = 17.5
k = 4, y = 28
k = 3, y = 21
First, calculate k as 15 ÷ 5 = 3. Then using y = kx, when x = 7, y = 3 × 7 = 21. This confirms the proportional relationship.
A scale factor is used to enlarge a diagram. If the constant of proportionality is 0.5 and the original length is 12, what is the new length?
18
4
12
6
Multiplying the original length by the scale factor gives the new length: 0.5 × 12 = 6. This keeps the proportions consistent.
Which of the following equations indicates that y is directly proportional to x with a constant of proportionality 1?
y = 2x
y = x/2
y = x
y = 0
The equation y = x shows a one-to-one correspondence between y and x, meaning the constant k is 1. This is the only option that represents direct proportionality with k = 1.
If y is directly proportional to x and when x = 9, y = 27, what is y when x = 15?
50
45
40
42
The constant k is 27 ÷ 9 = 3. With x increased to 15, y = 3 × 15 = 45, which maintains the proportionality.
In a proportional relationship, if 18 corresponds to 4, what number corresponds to 27?
7
8
5
6
Setting up the proportion 18/4 = 27/x and solving by cross multiplication gives x = (27 × 4) ÷ 18 = 6. This preserves the constant ratio.
A store sells pencils at a rate proportional to quantity. If 15 pencils cost $3, what is the cost for 40 pencils?
$8
$6
$9
$7
The cost per pencil is $3 ÷ 15 = $0.20. Multiplying the unit cost by 40 gives 40 × $0.20 = $8, which is the correct price.
If y = kx and the point (4, 10) lies on the graph, what are the coordinates when x = 7?
(7, 10)
(7, 20)
(7, 14)
(7, 17.5)
Find k by computing 10 ÷ 4 = 2.5. Then, for x = 7, y = 2.5 × 7 = 17.5, which gives the coordinate (7, 17.5).
What is the effect on the constant of proportionality if both x and y are multiplied by the same nonzero factor?
It remains unchanged
It doubles
It halves
It becomes zero
Multiplying both variables by the same factor does not change the ratio between them. Hence, the constant of proportionality remains the same.
Consider the proportion 7/14 = x/28. What is the value of x?
16
12
14
10
Since 7/14 simplifies to 1/2, setting 1/2 = x/28 leads to x = 28 ÷ 2 = 14, ensuring the ratio remains constant.
Which of the following equations represents a proportional relationship?
y = 5x
y = 3x + 2
y = x - 1
y = x^2
A proportional relationship must have the form y = kx with no additional constant. Only y = 5x meets this criterion.
A recipe uses a proportional relationship: 2 cups of sugar for every 5 cups of flour. If a baker wants to use 8 cups of sugar, how many cups of flour are needed?
18
22
16
20
Setting up the proportion 2/5 = 8/x and solving by cross multiplication gives x = (8 × 5) ÷ 2 = 20 cups of flour. This keeps the ingredients in proportion.
The graph of y = kx passes through (-3, 9). What is the constant k and what is y when x = -6?
k = -3 and y = -18
k = 3 and y = -18
k = 3 and y = 18
k = -3 and y = 18
For the point (-3, 9), k = 9 ÷ (-3) = -3. With k = -3, when x = -6 then y = -3 × (-6) = 18, confirming the proportional relationship.
In a proportional relationship between distance and time, if a car covers 150 miles in 3 hours at constant speed, how far will it travel in 5 hours?
225
250
275
200
The constant speed is 150 ÷ 3 = 50 miles per hour. Multiplying the speed by 5 hours gives 50 × 5 = 250 miles, ensuring the distance remains proportional to time.
If two variables are directly proportional and the constant of proportionality is 7/4, what is the value of y when x = 16?
30
28
24
32
Using y = (7/4)x, substitute x = 16 to obtain y = (7/4) × 16 = 28. This calculation confirms the proportional relationship.
A classroom's seating arrangement is proportional: 3 rows have 12 desks. How many desks will be in 7 rows if the proportion remains constant?
26
30
24
28
First, determine desks per row by dividing 12 by 3, which gives 4 desks per row. Multiplying 4 by 7 rows gives 28 desks, keeping the arrangement proportional.
0
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Study Outcomes

  1. Identify the constant of proportionality in various contexts.
  2. Apply proportional reasoning to solve real-world and mathematical problems.
  3. Analyze ratios to determine if relationships are proportional.
  4. Construct and simplify equations that represent proportional relationships.
  5. Interpret and evaluate scenarios using the principles of proportionality.

Constant of Proportionality Cheat Sheet

  1. Define Your Constant of Proportionality - The constant of proportionality, k, is the magic multiplier that links x and y in the formula y = kx. It tells you how many y's you get for each x, keeping the ratio rock‑steady every time. Third Space Learning guide
  2. Spot Proportional Relationships in Tables - Scan across rows of numbers and calculate y/x for each pair; if the ratio never wavers, you've got a proportional relationship on your hands. It's like checking that every slice of pizza is exactly the same size - consistency is key. Education.com worksheet
  3. Identify Proportional Graphs - Look for a straight line that rockets through the origin (0,0) - no off‑center starts allowed! That perfect linear path means y truly grows in lockstep with x. Third Space Learning guide
  4. Calculate k from a Table - Simply divide y by x for any row, and voilà - the answer is your constant k, as long as it stays constant across all rows. Think of it as tasting multiple spoonfuls of soup to make sure the flavor is exactly the same each time. Third Space Learning guide
  5. Determine k from a Graph - The slope of your line is the golden ticket: rise over run equals your constant of proportionality. Plot two clear points, calculate the rise/run, and you're set! Third Space Learning guide
  6. Apply k in Real‑World Problems - Use k to figure out speed (distance ÷ time) or unit price (cost ÷ quantity) with confidence - no more head‑scratching at the grocery store. Turn everyday puzzles into quick calculations. Maricopa Community College textbook
  7. Watch Out for Additive vs. Multiplicative Mix‑Ups - A common pitfall is treating a steady addition as if it were a proportional (multiplying) relationship. Remember: proportional means multiplication, not subtraction or addition! Common misconceptions
  8. Practice Cross‑Multiplying - To solve a proportion like a/b = c/d, cross‑multiply (a×d = b×c) and find the missing piece of the puzzle. It's like balancing a seesaw - once both sides match, you're done. Maricopa Community College textbook
  9. Compare with Unit Rates - Break down complex ratios to a "per‑one" basis (e.g., miles per gallon or cost per item) to make side‑by‑side comparisons a breeze. It's like converting every snack to a "per bite" price - suddenly the cheapest treat stands out. Maricopa Community College textbook
  10. Dive into Interactive Activities - Reinforce your skills with hands‑on exercises, quizzes, and games that bring proportional reasoning to life. Practice makes perfect, and you'll remember k like your favorite cheat code. Education.com worksheet
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