Middle School Math Quiz: Modeling Proportional Relationships
3 questions · exam conditions
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Modeling Proportional RelationshipsQuestion 1 of 3

Two quantities xx and yy are in a proportional relationship. When x=12x = 12, y=18y = 18. If this relationship is graphed and then translated 3 units up, what would be the equation of the new line?

y=1.5x+3y = 1.5x + 3
y=1.5x−3y = 1.5x - 3
y=1.5(x+3)y = 1.5(x + 3)
y=1.8xy = 1.8x
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Middle School Math Quiz

Middle School Math Quiz: Modeling Proportional Relationships

Practice Modeling Proportional Relationships 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 Modeling Proportional Relationships, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Two quantities xx and yy are in a proportional relationship. When x=12x = 12, y=18y = 18. If this relationship is graphed and then translated 3 units up, what would be the equation of the new line?

  1. y=1.5x+3y = 1.5x + 3 (correct answer)
  2. y=1.5x−3y = 1.5x - 3
  3. y=1.5(x+3)y = 1.5(x + 3)
  4. y=1.8xy = 1.8x
Explanation: First, find the constant of proportionality: k = y/x = 18/12 = 1.5, so the original equation is y = 1.5x. Translating 3 units up means adding 3 to the y-value: y = 1.5x + 3. Choice B translates down. Choice C translates horizontally (left 3 units). Choice D incorrectly changes the slope.

Question 2

A phone plan charges $0.15 per minute for calls. Which representation does NOT correctly model this proportional relationship where $mm representsminutesandrepresents minutes and CC $ represents total cost?

  1. The equation C=0.15mC = 0.15m
  2. A graph showing a line through (0,0) and (20,3)
  3. A table showing: 10 min/1.50,25min/1.50, 25 min/3.75, 40 min/$6.00
  4. A graph showing a line through (0,0) and (30,4) (correct answer)
Explanation: For $0.15 per minute: Choice A is correct equation. Choice B: 20 minutes costs 20 × $0.15 = $3.00 ✓. Choice C: All values check (10 × $0.15 = $1.50, etc.) ✓. Choice D: 30 minutes should cost 30 × $0.15 = $4.50, not $4.00 ✗. The point (30,4) represents $4.00 for 30 minutes, which gives an incorrect rate of $4.00/30 ≈ $0.133 per minute.

Question 3

A car rental company charges a flat fee plus a rate per mile. After driving 150 miles, the total cost is $85. After driving 300 miles, the total cost is $130. Which equation represents the proportional part of this relationship, where $yy isthevariablecostandis the variable cost and xx $ is the number of miles?

  1. y=0.3xy = 0.3x (correct answer)
  2. y=0.3x+40y = 0.3x + 40
  3. y=85x+150y = 85x + 150
  4. y=0.567xy = 0.567x
Explanation: First, find the rate per mile: (130 - 85) ÷ (300 - 150) = 45 ÷ 150 = 0.3. The proportional part represents only the variable cost, which is $0.30 per mile, so y = 0.3x. Choice B includes the flat fee, making it the total cost equation. Choice C reverses the variables. Choice D uses the incorrect rate 85/150.