Use the table to answer the question.

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 C is perpendicular to line D.
Line upper C is perpendicular to line upper D .

Line B is perpendicular to line D.
Line upper B is perpendicular to line upper D .

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

Line A is perpendicular to line C.

Answer 1

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

1. Line A: \( y = 2x - 3 \)

   • Slope: 2

2. Line B: \( y = 2x + 5 \)

   • Slope: 2

3. Line C: \( y = -12x - 2 \)

   • Slope: -12

4. Line D: \( y = 12x + 2 \)

   • Slope: 12

Now we can analyze each pair:

• Line A and Line B:
  Both have a slope of 2.
  \(2 \times 2 = 4\) (not perpendicular)

• Line C and Line D:
  Slope of Line C is -12 and slope of Line D is 12.
  \(-12 \times 12 = -144\) (not perpendicular)

• Line A and Line C:
  Slope of Line A is 2 and slope of Line C is -12.
  \(2 \times -12 = -24\) (not perpendicular)

• Line B and Line D:
  Slope of Line B is 2 and slope of Line D is 12.
  \(2 \times 12 = 24\) (not perpendicular)

Since none of the lines are perpendicular based on their slopes, none of the statements provided are true. However, to clarify:

• Line C is parallel to Line D because their slopes multiply to 1.
• Line A and Line B are also parallel.

Conclusion: None of the options provided are true based on the slopes of the lines given.