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If two lines are parallel and one line has the equation y = 5x + 1, what is the

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Question: If two lines are parallel and one line has the equation y = 5x + 1, what is the equation of a line parallel to it that passes through the point (2, 3)?

Options:

  1. y = 5x - 7
  2. y = 5x + 7
  3. y = 5x + 1
  4. y = 5x - 1

Correct Answer: y = 5x - 7

Solution: 

A line parallel to y = 5x + 1 will have the same slope (5). Using the point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.

If two lines are parallel and one line has the equation y = 5x + 1, what is the

Practice Questions

Q1
If two lines are parallel and one line has the equation y = 5x + 1, what is the equation of a line parallel to it that passes through the point (2, 3)?
  1. y = 5x - 7
  2. y = 5x + 7
  3. y = 5x + 1
  4. y = 5x - 1

Questions & Step-by-Step Solutions

If two lines are parallel and one line has the equation y = 5x + 1, what is the equation of a line parallel to it that passes through the point (2, 3)?
  • Step 1: Identify the slope of the given line. The equation is y = 5x + 1, so the slope (m) is 5.
  • Step 2: Since parallel lines have the same slope, the slope of the new line will also be 5.
  • Step 3: Use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Here, (x1, y1) is (2, 3).
  • Step 4: Substitute the slope and the point into the point-slope form: y - 3 = 5(x - 2).
  • Step 5: Simplify the equation. Distribute the 5: y - 3 = 5x - 10.
  • Step 6: Add 3 to both sides to solve for y: y = 5x - 10 + 3.
  • Step 7: Combine like terms: y = 5x - 7.
  • Step 8: The final equation of the line parallel to y = 5x + 1 that passes through (2, 3) is y = 5x - 7.
  • Parallel Lines – Parallel lines have the same slope, which is crucial for finding the equation of a line parallel to a given line.
  • Point-Slope Form – The point-slope form of a line is used to find the equation of a line given a point and the slope.
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