Question

Given the table below, which of the following statements is true?

Line Equation
Line A y=−12x−2
Line B y=2x−3
Line C y=12x+2
Line D y=2x+5



(1 point)
Responses

Line C is perpendicular to Line D
Line C is perpendicular to Line D

Line B is perpendicular to Line D
Line B is perpendicular to Line D

Line A is perpendicular to Line C
Line A is perpendicular to Line C

Line A is perpendicular to Line B

Answer 1

To determine which statements are true regarding the lines, we first need to identify the slopes of each line from their equations.

The slope-intercept form of a line is given by the equation \(y = mx + b\), where \(m\) represents the slope.

Here are the slopes for each line:

- **Line A:** \(y = -12x - 2\) → Slope = -12
- **Line B:** \(y = 2x - 3\) → Slope = 2
- **Line C:** \(y = 12x + 2\) → Slope = 12
- **Line D:** \(y = 2x + 5\) → Slope = 2

Next, we recall that two lines are perpendicular if the product of their slopes is equal to -1.

Now, we can evaluate the statements:

1. **Line C is perpendicular to Line D:**
- Slope of Line C = 12
- Slope of Line D = 2
- \(12 \times 2 \neq -1\) → Not true.

2. **Line B is perpendicular to Line D:**
- Slope of Line B = 2
- Slope of Line D = 2
- \(2 \times 2 \neq -1\) → Not true.

3. **Line A is perpendicular to Line C:**
- Slope of Line A = -12
- Slope of Line C = 12
- \(-12 \times 12 \neq -1\) → Not true.

4. **Line A is perpendicular to Line B:**
- Slope of Line A = -12
- Slope of Line B = 2
- \(-12 \times 2 = -24 \neq -1\) → Not true.

Based on the analysis, none of the provided statements are true. However, if I misunderstood the context of the question or if the range of possible responses was broader, please clarify, and I'll gladly reevaluate.