Question

Question 1
Line Equation
Line A y= 2x-3
Line B y= 2x + 5
Line C y= -1/2x - 2
Line D y= 1/2x + 2

Given the linear equation in the table, which of the following statements is true?
A. Line C is perpendicular to line D.
B. Line B is perpendicular to line D.
C. Line A is perpendicular to line C. C is the correct answer.
D. Line A is perpendicular to line B.

Question 2
Line Equation
Line A y= -3x -2
Line B y= 3x + 4
Line C y= -1/3x -2
Line D y= 1/3x + 4

Select the correct answer
Given the linear equation in the table, which of the following statements is true?
(1 point)
* Line A is perpendicular to line D.
* Line A is perpendicular to line B.
* Line B is perpendicular to line D.
* Line A is perpendicular to line C.

Answer 1

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

### Question 1
**Equations:**
- Line A: \(y = 2x - 3\) (slope = 2)
- Line B: \(y = 2x + 5\) (slope = 2)
- Line C: \(y = -\frac{1}{2}x - 2\) (slope = -\frac{1}{2})
- Line D: \(y = \frac{1}{2}x + 2\) (slope = \frac{1}{2})

**Checking slopes:**
- The slopes of lines A and B are the same (2), so they are parallel.
- Line C has a slope of -\(\frac{1}{2}\) and Line D has a slope of \(\frac{1}{2}\). The product of these slopes is:
\[
-\frac{1}{2} \times \frac{1}{2} = -\frac{1}{4} \quad (\text{not perpendicular})
\]
- Line A (2) and Line C (-\(\frac{1}{2}\)):
\[
2 \times -\frac{1}{2} = -1 \quad (\text{perpendicular})
\]
- Line B (2) and Line C (-\(\frac{1}{2}\)):
\[
2 \times -\frac{1}{2} = -1 \quad (\text{perpendicular})
\]

**Conclusion for Question 1:**
- C. Line A is perpendicular to Line C. (This is true)

### Question 2
**Equations:**
- Line A: \(y = -3x - 2\) (slope = -3)
- Line B: \(y = 3x + 4\) (slope = 3)
- Line C: \(y = -\frac{1}{3}x - 2\) (slope = -\frac{1}{3})
- Line D: \(y = \frac{1}{3}x + 4\) (slope = \(\frac{1}{3}\))

**Checking slopes:**
- Line A (-3) and Line D (\(\frac{1}{3}\)):
\[
-3 \times \frac{1}{3} = -1 \quad (\text{perpendicular})
\]
- Line A (-3) and Line B (3):
\[
-3 \times 3 = -9 \quad (\text{not perpendicular})
\]
- Line B (3) and Line D (\(\frac{1}{3}\)):
\[
3 \times \frac{1}{3} = 1 \quad (\text{not perpendicular})
\]
- Line A (-3) and Line C (-\(\frac{1}{3}\)):
\[
-3 \times -\frac{1}{3} = 1 \quad (\text{not perpendicular})
\]

**Conclusion for Question 2:**
- Line A is perpendicular to Line D.

### Summary of Answers:
- **Question 1:** C. Line A is perpendicular to line C.
- **Question 2:** Line A is perpendicular to line D.