Question

Use the table to answer the question.

Linear Equations of Different Lines
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 which of the statements is true regarding the lines represented by the equations, we need to analyze their slopes.

**Step 1: Identify the slopes of the lines.**
- For Line A (y = 2x - 3), the slope is 2.
- For Line B (y = 2x + 5), the slope is also 2.
- For Line C (y = -12x - 2), the slope is -12.
- For Line D (y = 12x + 2), the slope is 12.

**Step 2: Check for perpendicular lines.**
Two lines are perpendicular if the product of their slopes is -1.

- **Line A and Line B**: Both have a slope of 2.
\[ 2 * 2 = 4 \quad \text{(not perpendicular)} \]

- **Line C and Line D**: Slopes are -12 and 12.
\[ -12 * 12 = -144 \quad \text{(not perpendicular)} \]

- **Line B and Line D**: Slopes are 2 and 12.
\[ 2 * 12 = 24 \quad \text{(not perpendicular)} \]

- **Line A and Line C**: Slopes are 2 and -12.
\[ 2 * (-12) = -24 \quad \text{(not perpendicular)} \]

**Conclusion:**
None of the given pairs of lines are perpendicular to each other. Therefore, the correct answer is:

None of the statements provided are true.