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

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

Line B is perpendicular to line D.

Answer 1

To determine which lines are perpendicular, we need to look at the slopes of the lines given in their equations.

The standard form of a linear equation is \(y = mx + b\), where \(m\) is the slope.

From the equations provided:

- Line A: \(y = 2x - 3\) → slope \(m_A = 2\)
- Line B: \(y = 2x + 5\) → slope \(m_B = 2\)
- Line C: \(y = -12x - 2\) → slope \(m_C = -12\)
- Line D: \(y = 12x + 2\) → slope \(m_D = 12\)

Two lines are perpendicular if the product of their slopes is \(-1\) (i.e., \(m_1 \times m_2 = -1\)).

Now, let's analyze the pairs:

1. **Line C and Line D**:
- \(m_C \times m_D = -12 \times 12 = -144\) (not perpendicular)

2. **Line A and Line C**:
- \(m_A \times m_C = 2 \times -12 = -24\) (not perpendicular)

3. **Line A and Line B**:
- \(m_A \times m_B = 2 \times 2 = 4\) (not perpendicular)

4. **Line B and Line D**:
- \(m_B \times m_D = 2 \times 12 = 24\) (not perpendicular)

None of the given lines are perpendicular to each other since none of the products of their slopes equals \(-1\).

Based on the original statements provided, all of them would be false. Therefore, none of the selected relations between the lines accurately represents perpendicularity.