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Which of the following equations represent parallel lines?

  1. 4x + 7y = 0 and 4x + 7y = 10

  2. 4x + 7y = 0 and 7x - 4y = 12

  3. 7x - 4y = 0 and 4x + 7y = 10

  4. 4x + 7y = 0 and 4x - 7y = 10

The correct answer is: 4x + 7y = 0 and 4x - 7y = 10

Parallel lines are defined as lines that are always the same distance apart and never intersect. This means that they have the same slope. Option A and B have the same slope, but different y-intercepts, so they are not parallel. Option C has a different slope, so they are not parallel. Only option D has both the same slope and the same y-intercept, making the equations represent parallel lines.