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 if the given lines are perpendicular, we need to look at the slopes of the lines, as two lines are perpendicular if the product of their slopes is -1.

From the equations given:

- 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 let's analyze the relationships between the slopes:

1. **Line A and Line B**: Both have a slope of 2. Since \( 2 \times 2 = 4 \) (not -1), they are not perpendicular.
2. **Line C and Line D**: The slope of Line C is -12 and the slope of Line D is 12. Since \( -12 \times 12 = -144 \) (not -1), they are not perpendicular.
3. **Line B and Line D**: The slope of Line B is 2 and the slope of Line D is 12. Since \( 2 \times 12 = 24 \) (not -1), they are not perpendicular.
4. **Line A and Line C**: The slope of Line A is 2 and the slope of Line C is -12. Since \( 2 \times -12 = -24 \) (not -1), they are not perpendicular.

Based on the calculations, none of the lines listed correspond to perpendicular lines. It appears there might be a misinterpretation or error in the options provided, but none of the statements are true.