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What is the equation of the line that is perpendicular to y = 3x + 4 and passes

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Question: What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)

Options:

  1. y - 1 = -1/3(x - 1)
  2. y - 1 = 3(x - 1)
  3. y - 1 = 3/1(x - 1)
  4. y - 1 = -3(x - 1)

Correct Answer: y - 1 = -1/3(x - 1)

Exam Year: 2022

Solution: 

The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1).

What is the equation of the line that is perpendicular to y = 3x + 4 and passes

Practice Questions

Q1
What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)
  1. y - 1 = -1/3(x - 1)
  2. y - 1 = 3(x - 1)
  3. y - 1 = 3/1(x - 1)
  4. y - 1 = -3(x - 1)

Questions & Step-by-Step Solutions

What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)
  • Step 1: Identify the slope of the given line y = 3x + 4. The slope (m) is 3.
  • Step 2: Find the slope of the line that is perpendicular to the given line. The slope of a perpendicular line is the negative reciprocal of the original slope. So, the negative reciprocal of 3 is -1/3.
  • Step 3: Use the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. Here, (x1, y1) is (1, 1) and m is -1/3.
  • Step 4: Substitute the values into the point-slope form: y - 1 = -1/3(x - 1).
  • Step 5: This is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1).
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