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 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.

Answer 1

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.