Question

Select the equation that is not parallel or perpendicular to the line

y=-2x+5 and has a y intercept of -5

a
y=(1/2)x-5

b
y=x-5

c
y=4x-5

Answer 1

To determine which equation is not parallel or perpendicular to the line \( y = -2x + 5 \) and has a y-intercept of -5, we first analyze the properties of the given line.

1. **Slope of the given line**: The slope of the line \( y = -2x + 5 \) is -2.

2. **Parallel lines**: Lines that are parallel have the same slope. Therefore, any line parallel to \( y = -2x + 5 \) will also have a slope of -2.

3. **Perpendicular lines**: Lines that are perpendicular to it will have slopes that are negative reciprocals. The negative reciprocal of -2 is \( \frac{1}{2} \).

4. **Y-intercept requirement**: We are looking for equations with a y-intercept of -5.

Now we will review the options given:

a) \( y = \frac{1}{2}x - 5 \)
- Slope: \( \frac{1}{2} \) (This is perpendicular to the line since it is the negative reciprocal of -2,)
- Y-intercept: -5

b) \( y = x - 5 \)
- Slope: 1 (This is neither parallel nor perpendicular to the line which has a slope of -2)
- Y-intercept: -5

c) \( y = 4x - 5 \)
- Slope: 4 (This is neither parallel nor perpendicular to the line which has a slope of -2)
- Y-intercept: -5

In conclusion, options (b) and (c) have slopes that do not match the parallel or perpendicular criteria. However, we need to select one option that is definitely not parallel or perpendicular.

Option **b** \( y = x - 5 \) has a slope of 1 and is the only option that is neither parallel nor perpendicular to the original line.

Therefore, the final answer is:

**b) \( y = x - 5 \)**