Question

Select the equation that is not parallel nor perpendicular to the given

equation: y=-0.5x+8

a
y=(1/2)x+9

b
y=2x+2

c
y=(-1/2)x+3

Answer 1

To determine which of the provided equations is neither parallel nor perpendicular to the given equation \( y = -0.5x + 8 \), we first need to understand the slope of the given equation.

1. **Identify the slope of the given equation:**
- The equation \( y = -0.5x + 8 \) has a slope \( m = -0.5 \).

2. **Determine the conditions for parallel and perpendicular lines:**
- **Parallel lines** have the same slope. Thus, any equation with a slope of \(-0.5\) will be parallel.
- **Perpendicular lines** have slopes that are negative reciprocals of each other. For a slope of \(-0.5\), the negative reciprocal would be \(2\) (since \(-\frac{1}{-0.5} = 2\)).

3. **Evaluate each option:**

a. **For \( y = \frac{1}{2}x + 9 \):**
- The slope is \( m = \frac{1}{2} \).
- This is neither equal to \(-0.5\) (not parallel) nor \(2\) (not perpendicular).

b. **For \( y = 2x + 2 \):**
- The slope is \( m = 2 \).
- This is perpendicular to the original slope of \(-0.5\).

c. **For \( y = -\frac{1}{2}x + 3 \):**
- The slope is \( m = -\frac{1}{2} \).
- This is parallel since it is equal to \(-0.5\) (but reversed).

4. **Conclusion:**
- From the analysis above, the equation that is neither parallel nor perpendicular to the given equation \( y = -0.5x + 8 \) is:

**a. \( y = \frac{1}{2}x + 9 \)**.