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

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

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

Line A
is perpendicular to line B
.

Answer 1

To determine which of the statements is true regarding the lines, we need to check the slopes of the lines provided in the equations.

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

Here are the slopes of the lines:

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

Lines are perpendicular if the product of their slopes is \(-1\). So we can evaluate the pairs:

1. **Line A and Line B**:
\( 2 \times 2 = 4 \) (not perpendicular)

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

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

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

Since none of the lines are perpendicular to each other according to their slopes, all statements provided are false.

Therefore, the answer is: **None of the statements are true**.