witch one is right

Question

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

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

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

Line A is perpendicular to line C.

Answer 1

To determine which statements about the lines are true, we need to analyze the slopes of the given lines. The equations of the lines are:

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)

Two lines are perpendicular if the product of their slopes is -1. Let's evaluate the pairs:

1. Line A (slope = 2) and Line B (slope = 2):

   • \( 2 \times 2 = 4 \) (not perpendicular)

2. Line C (slope = -12) and Line D (slope = 12):

   • \( -12 \times 12 = -144 \) (not perpendicular)

3. Line B (slope = 2) and Line D (slope = 12):

   • \( 2 \times 12 = 24 \) (not perpendicular)

4. Line A (slope = 2) and Line C (slope = -12):

   • \( 2 \times -12 = -24 \) (not perpendicular)

Since none of the pairs of lines are perpendicular to each other, it appears that none of the statements in the question are true.

If we need to select the best answer and all options provided are incorrect, then that must be interpreted as the conclusion.

However, if you must choose one of the provided statements for the sake of answering, you could simply say that none of them is true.