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SAT Math: Linear Equations (Drill 3)

Drill 3 · Math · Linear Equations

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About This Drill

SAT Math: Linear Equations (Drill 3) is a Math practice drill covering Linear Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT linear equation questions cover solving equations, interpreting slope and y-intercept in context, writing equations from verbal descriptions, and working with parallel and perpendicular lines. This drill emphasizes translating real-world scenarios into linear models.

Questions & Explanations

Question 1. A plumber charges a $75 service fee plus $50 per hour. Which equation represents the total cost C for h hours of work?

  • A) C = 75h + 50
  • B) C = 50h + 75 ✓
  • C) C = 125h
  • D) C = 50h − 75

Explanation: The fixed fee ($75) is the y-intercept and the hourly rate ($50) is the slope: C = 50h + 75.

Question 2. What is the x-intercept of the line 3x − 4y = 24?

  • A) (8, 0) ✓
  • B) (0, −6)
  • C) (6, 0)
  • D) (24, 0)

Explanation: Set y = 0: 3x = 24, x = 8. The x-intercept is (8, 0).

Question 3. Line m has slope 2/3. What is the slope of a line perpendicular to line m?

  • A) 2/3
  • B) −2/3
  • C) 3/2
  • D) −3/2 ✓

Explanation: Perpendicular lines have slopes that are negative reciprocals. The negative reciprocal of 2/3 is −3/2.

Question 4. If 5(x − 2) + 3 = 2(x + 4), what is x?

  • A) 3
  • B) 5 ✓
  • C) 4
  • D) 2

Explanation: 5x − 10 + 3 = 2x + 8. Simplify: 5x − 7 = 2x + 8. 3x = 15. x = 5.

Question 5. A tank contains 500 gallons of water and is draining at 15 gallons per minute. After how many minutes will the tank have 200 gallons remaining?

  • A) 15
  • B) 20 ✓
  • C) 25
  • D) 30

Explanation: 500 − 15t = 200. 15t = 300. t = 20 minutes.