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

Answer 1

To determine which lines are perpendicular, we need to examine the slopes of each line. Lines are perpendicular if the product of their slopes equals -1.

1. **Line A: y = 2x - 3**
- Slope (m) = 2

2. **Line B: y = 2x + 5**
- Slope (m) = 2

3. **Line C: y = -12x - 2**
- Slope (m) = -12

4. **Line D: y = 12x + 2**
- Slope (m) = 12

Now we'll check the products of the slopes:

- Lines A and B both have a slope of 2:
\( 2 \times 2 = 4 \) (not perpendicular)

- Lines A and C:
\( 2 \times -12 = -24 \) (not perpendicular)

- Lines A and D:
\( 2 \times 12 = 24 \) (not perpendicular)

- Lines B and C:
\( 2 \times -12 = -24 \) (not perpendicular)

- Lines B and D:
\( 2 \times 12 = 24 \) (not perpendicular)

- Lines C and D:
\( -12 \times 12 = -144 \) (not perpendicular)

Since none of the lines' slopes produce a product of -1, **none of the lines are perpendicular** to each other. Therefore, there is no true statement among the options provided.