Question

Determine if the sign is parallel perpendicular or neither

Y = -1/4 x
Y = 4x - 5

Answer 1

To determine if the lines given by the equations \( y = -\frac{1}{4}x \) and \( y = 4x - 5 \) are parallel, perpendicular, or neither, we need to look at their slopes.

1. **Finding the slope of the first line \( y = -\frac{1}{4}x \)**:
- The slope \( m_1 \) of this line is \(-\frac{1}{4}\).

2. **Finding the slope of the second line \( y = 4x - 5 \)**:
- The slope \( m_2 \) of this line is \(4\).

3. **Comparison of the slopes**:
- Two lines are **parallel** if their slopes are equal, i.e., \( m_1 = m_2 \).
- Two lines are **perpendicular** if the product of their slopes is \(-1\), i.e., \( m_1 \cdot m_2 = -1\).

Now, let's check:

- The slopes are \( m_1 = -\frac{1}{4} \) and \( m_2 = 4 \).

Calculating the product of the slopes:
\[
m_1 \cdot m_2 = -\frac{1}{4} \cdot 4 = -1
\]

Since the product of the slopes is \(-1\), the lines are **perpendicular**.

**Conclusion**: The lines \( y = -\frac{1}{4}x \) and \( y = 4x - 5 \) are perpendicular.