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If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of interse

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Question: If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?

Options:

  1. (0, 3)
  2. (0, -3)
  3. (0, 4)
  4. (0, -4)

Correct Answer: (0, -4)

Solution: 

Setting x = 0 gives -4y + 12 = 0, thus y = -3. The point of intersection is (0, -3).

If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of interse

Practice Questions

Q1
If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?
  1. (0, 3)
  2. (0, -3)
  3. (0, 4)
  4. (0, -4)

Questions & Step-by-Step Solutions

If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?
  • Step 1: Understand that the y-axis is where x = 0.
  • Step 2: Substitute x = 0 into the equation 3x - 4y + 12 = 0.
  • Step 3: This gives us the equation -4y + 12 = 0.
  • Step 4: Rearrange the equation to solve for y by moving 12 to the other side: -4y = -12.
  • Step 5: Divide both sides by -4 to find y: y = -12 / -4.
  • Step 6: Simplify the division: y = 3.
  • Step 7: The point of intersection on the y-axis is (0, 3).
  • Line Equation – Understanding how to find the intersection of a line with the y-axis by setting x to 0.
  • Coordinate Geometry – Applying knowledge of coordinates to determine points of intersection in a Cartesian plane.
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