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 about the lines based on their equations, we need to find the slopes of each line.

The general form of a line's equation is \( y = mx + b \), where \( m \) is the slope.

The slopes from the equations provided are:
- Line A: \( y = -12x - 2 \) → slope \( m_A = -12 \)
- Line B: \( y = 2x - 3 \) → slope \( m_B = 2 \)
- Line C: \( y = 12x + 2 \) → slope \( m_C = 12 \)
- Line D: \( y = 2x + 5 \) → slope \( m_D = 2 \)

Next, to check for perpendicularity, we remember that two lines are perpendicular if the product of their slopes is -1.

1. For Line A and Line C:
\[
m_A \cdot m_C = (-12) \cdot 12 = -144 \quad (\text{not perpendicular})
\]

2. For Line A and Line B:
\[
m_A \cdot m_B = (-12) \cdot 2 = -24 \quad (\text{not perpendicular})
\]

3. For Line B and Line D:
\[
m_B \cdot m_D = 2 \cdot 2 = 4 \quad (\text{not perpendicular})
\]

4. For Line C and Line D:
\[
m_C \cdot m_D = 12 \cdot 2 = 24 \quad (\text{not perpendicular})
\]

None of the pairs of lines are perpendicular. Thus, based on the given options, **none of the statements are true**.

If we assume that the answer must come from one of the listed statements and acknowledge the errors in the context of this question, **the analysis would indicate that all proposed statements regarding perpendicular lines are incorrect based on their slopes.**