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

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

Options:

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

Correct Answer: -3/4

Solution: 

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

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

Practice Questions

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

Questions & Step-by-Step Solutions

If the line 3x - 4y + 12 = 0 is parallel to another line, what is the slope of the parallel line?
  • Step 1: Start with the equation of the line: 3x - 4y + 12 = 0.
  • Step 2: Rearrange the equation to solve for y. Move 3x and 12 to the other side: -4y = -3x - 12.
  • Step 3: Divide every term by -4 to isolate y: y = (3/4)x + 3.
  • Step 4: Identify the slope from the equation y = (3/4)x + 3. The slope is 3/4.
  • Step 5: Remember that parallel lines have the same slope. Therefore, the slope of the parallel line is also 3/4.
  • Slope of a Line – Understanding that parallel lines have the same slope.
  • Rearranging Linear Equations – Ability to manipulate the equation of a line into slope-intercept form (y = mx + b).
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