Middle School Math Quiz: Writing Linear Equations Y Equals Mx Plus B
4 questions · exam conditions
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Writing Linear Equations Y Equals Mx Plus BQuestion 1 of 4

A delivery service charges based on package weight. For a 5-pound package, the cost is $18. For a 12-pound package, the cost is $32. Assuming the relationship is linear, which equation represents the cost $yy forapackageweighingfor a package weighing xx $ pounds?

y=2x+8y = 2x + 8
y=3x+3y = 3x + 3
y=1.5x+10.5y = 1.5x + 10.5
y=2.5x+5.5y = 2.5x + 5.5
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Middle School Math Quiz: Writing Linear Equations Y Equals Mx Plus B

Practice Writing Linear Equations Y Equals Mx Plus B 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 Writing Linear Equations Y Equals Mx Plus B, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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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.

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Question 1

A delivery service charges based on package weight. For a 5-pound package, the cost is $18. For a 12-pound package, the cost is $32. Assuming the relationship is linear, which equation represents the cost $yy forapackageweighingfor a package weighing xx $ pounds?

  1. y=2x+8y = 2x + 8 (correct answer)
  2. y=3x+3y = 3x + 3
  3. y=1.5x+10.5y = 1.5x + 10.5
  4. y=2.5x+5.5y = 2.5x + 5.5
Explanation: Using points (5,18) and (12,32), the slope is m=32−1812−5=147=2m = \frac{32-18}{12-5} = \frac{14}{7} = 2. Using point-slope form with (5,18): y−18=2(x−5)y - 18 = 2(x - 5), which gives y=2x+8y = 2x + 8. This means $8 base charge plus $2 per pound. Verify: for 12 pounds, $y=2(12)+8=32y = 2(12) + 8 = 32 ✓.ChoiceBgives✓. Choice B gives y=3(5)+3=18y = 3(5) + 3 = 18 ✓but✓ but y=3(12)+3=39≠32y = 3(12) + 3 = 39 \neq 32 .ChoiceCgives. Choice C gives y=1.5(5)+10.5=18y = 1.5(5) + 10.5 = 18 ✓but✓ but y=1.5(12)+10.5=28.5≠32y = 1.5(12) + 10.5 = 28.5 \neq 32 .ChoiceDgives. Choice D gives y=2.5(5)+5.5=18y = 2.5(5) + 5.5 = 18 ✓but✓ but y=2.5(12)+5.5=35.5≠32y = 2.5(12) + 5.5 = 35.5 \neq 32 $.

Question 2

A water tank initially contains 150 gallons and drains at a constant rate. After 4 hours, it contains 110 gallons. After 9 hours, it contains 60 gallons. Which equation models the amount of water yy (in gallons) remaining after xx hours?

  1. y=−10x+150y = -10x + 150 (correct answer)
  2. y=−12x+158y = -12x + 158
  3. y=−8x+142y = -8x + 142
  4. y=−15x+170y = -15x + 170
Explanation: Using points (4,110) and (9,60), the slope is m=60−1109−4=−505=−10m = \frac{60-110}{9-4} = \frac{-50}{5} = -10. Using point-slope form with (4,110): y−110=−10(x−4)y - 110 = -10(x - 4), which gives y=−10x+150y = -10x + 150. This means the tank starts with 150 gallons (when x=0x = 0) and drains 10 gallons per hour. Verify: at x=4x = 4, y=−10(4)+150=110y = -10(4) + 150 = 110 ✓; at x=9x = 9, y=−10(9)+150=60y = -10(9) + 150 = 60 ✓. The other choices give incorrect values when substituted.

Question 3

A candle burns at a constant rate. Initially it is 8 inches tall. After burning for 3 hours, it is 6.5 inches tall. After burning for 7 hours, it is 4.5 inches tall. Which equation models the candle's height yy (in inches) after burning for xx hours?

  1. y=−0.5x+8y = -0.5x + 8 (correct answer)
  2. y=−0.4x+8.2y = -0.4x + 8.2
  3. y=−0.6x+7.8y = -0.6x + 7.8
  4. y=−0.75x+8.25y = -0.75x + 8.25
Explanation: Using points (3, 6.5) and (7, 4.5), the slope is m=4.5−6.57−3=−24=−0.5m = \frac{4.5-6.5}{7-3} = \frac{-2}{4} = -0.5. Since the candle starts at 8 inches when x=0x = 0, the y-intercept is 8. Therefore, y=−0.5x+8y = -0.5x + 8. Verify: at x=3x = 3, y=−0.5(3)+8=6.5y = -0.5(3) + 8 = 6.5 ✓; at x=7x = 7, y=−0.5(7)+8=4.5y = -0.5(7) + 8 = 4.5 ✓. The candle burns 0.5 inches per hour. Other choices give incorrect heights when substituted.

Question 4

A parking garage charges a flat entrance fee plus an hourly rate. The total cost for parking 3 hours is $12, and the total cost for parking 7 hours is $20. If $yy representsthetotalcostandrepresents the total cost and xx $ represents the number of hours, which equation represents this situation?

  1. y=2x+6y = 2x + 6 (correct answer)
  2. y=3x+3y = 3x + 3
  3. y=4x+0y = 4x + 0
  4. y=6x−6y = 6x - 6
Explanation: First find the slope: m=20−127−3=84=2m = \frac{20-12}{7-3} = \frac{8}{4} = 2. Then use point-slope form with (3,12): y−12=2(x−3)y - 12 = 2(x - 3), which simplifies to y=2x+6y = 2x + 6. We can verify: when x=3x = 3, y=2(3)+6=12y = 2(3) + 6 = 12 ✓, and when x=7x = 7, y=2(7)+6=20y = 2(7) + 6 = 20 ✓. Choice B gives incorrect values (y=3(3)+3=12y = 3(3) + 3 = 12 works but y=3(7)+3=24≠20y = 3(7) + 3 = 24 \neq 20). Choice C gives y=4(3)=12y = 4(3) = 12 but y=4(7)=28≠20y = 4(7) = 28 \neq 20. Choice D gives y=6(3)−6=12y = 6(3) - 6 = 12 but y=6(7)−6=36≠20y = 6(7) - 6 = 36 \neq 20.