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uestion Line Equation Line A y= 2x −3 Line B y= 2x + 5 Line C y= −12x −2 Line D y= 12x + 2 Given the linear equation in the table, which of the following statements is true? (1 point) Responses Line A is perpendicular to line B. Line A is perpendicular to line B. Line A is perpendicular to line C. Line A is perpendicular to line C. Line C is perpendicular to line D. Line C is perpendicular to line D. Line B is perpendicular to line D. Line B is perpendicular to line D. Skip to navigation

1 answer

To determine which lines are perpendicular, we need to look at their slopes. Two lines are perpendicular if the product of their slopes is -1.

Here are the slopes of the lines based on their equations:

  • Line A: \( y = 2x - 3 \) → slope = 2
  • Line B: \( y = 2x + 5 \) → slope = 2
  • Line C: \( y = -12x - 2 \) → slope = -12
  • Line D: \( y = 12x + 2 \) → slope = 12

Now, we can check the products of the slopes:

  1. Line A and Line B:
    \( 2 \times 2 = 4 \) (not perpendicular)

  2. Line A and Line C:
    \( 2 \times -12 = -24 \) (not perpendicular)

  3. Line C and Line D:
    \( -12 \times 12 = -144 \) (not perpendicular)

  4. Line B and Line D:
    \( 2 \times 12 = 24 \) (not perpendicular)

None of the pairs of lines are perpendicular to each other based on their slopes.

So the correct answer is that none of the statements provided are true.