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If the line 4x - 3y + 12 = 0 is parallel to another line, what is the slope of t

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Question: If the line 4x - 3y + 12 = 0 is parallel to another line, what is the slope of the parallel line? (2022)

Options:

  1. 4/3
  2. 3/4
  3. -4/3
  4. -3/4

Correct Answer: -4/3

Exam Year: 2022

Solution: 

Rearranging gives y = (4/3)x + 4. The slope is -4/3, so a parallel line has the same slope.

If the line 4x - 3y + 12 = 0 is parallel to another line, what is the slope of t

Practice Questions

Q1
If the line 4x - 3y + 12 = 0 is parallel to another line, what is the slope of the parallel line? (2022)
  1. 4/3
  2. 3/4
  3. -4/3
  4. -3/4

Questions & Step-by-Step Solutions

If the line 4x - 3y + 12 = 0 is parallel to another line, what is the slope of the parallel line? (2022)
  • Step 1: Start with the equation of the line: 4x - 3y + 12 = 0.
  • Step 2: Rearrange the equation to solve for y. Move 4x and 12 to the other side: -3y = -4x - 12.
  • Step 3: Divide every term by -3 to isolate y: y = (4/3)x + 4.
  • Step 4: Identify the slope from the equation y = (4/3)x + 4. The slope is the coefficient of x, which is 4/3.
  • Step 5: Remember that parallel lines have the same slope. Therefore, the slope of the parallel line is also 4/3.
  • Slope of a Line – Understanding that the slope of a line in the form Ax + By + C = 0 can be derived by rearranging it into slope-intercept form (y = mx + b), where m is the slope.
  • Parallel Lines – Recognizing that parallel lines have identical slopes.
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