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Use the table to answer the question.

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 equations in the table, which of the following statements is true?

(1 point)
Responses

Line A is perpendicular to line C.
Line A is perpendicular to line C .

Line A is perpendicular to line B.
Line A is perpendicular to line B .

Line B is perpendicular to line D.

1 answer

To determine which statements about the lines are true, we need to look at the slopes of the lines given by their equations. The slope of a line in the form \( y = mx + b \) is represented by \( m \).

  • 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

Two lines are perpendicular if the product of their slopes is -1.

  1. Line A and Line C:

    • Slope of Line A = 2
    • Slope of Line C = -12
    • Product = \( 2 \times -12 = -24 \) (not perpendicular)

  2. Line A and Line B:

    • Slope of Line A = 2
    • Slope of Line B = 2
    • Product = \( 2 \times 2 = 4 \) (not perpendicular)

  3. Line B and Line D:

    • Slope of Line B = 2
    • Slope of Line D = 12
    • Product = \( 2 \times 12 = 24 \) (not perpendicular)

None of the lines are perpendicular to each other. Therefore, all the provided statements about the lines being perpendicular are false.

Thus, none of the statements are true.