Question

y=1/4x-2
y=-4x-1
paralel, perpendicular or neither

Answer 1

break it down simplier without the extra symbols

Answer 2

To determine whether the lines represented by the equations \( y = \frac{1}{4}x - 2 \) and \( y = -4x - 1 \) are parallel, perpendicular, or neither, we need to analyze their slopes.

1. **Identify the slope of each line:**

- For the first equation \( y = \frac{1}{4}x - 2 \), the slope \( m_1 \) is \( \frac{1}{4} \).
- For the second equation \( y = -4x - 1 \), the slope \( m_2 \) is \( -4 \).

2. **Determine if the lines are parallel, perpendicular, or neither:**

- Lines are **parallel** if their slopes are equal: \( m_1 = m_2 \).
- Lines are **perpendicular** if the product of their slopes is \(-1\): \( m_1 \cdot m_2 = -1 \).

Now, calculate 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**.

Answer 3

Sure! Let's break it down step by step in simpler terms:

1. **Look at the first line**: The equation is \(y = \frac{1}{4}x - 2\). The slope (the number in front of \(x\)) is **1/4**.

2. **Look at the second line**: The equation is \(y = -4x - 1\). The slope here is **-4**.

3. **Compare the slopes**:
- If the slopes are the same, the lines are **parallel**.
- If the slopes multiply to give **-1**, the lines are **perpendicular**.
- If neither of these is true, then the lines are **neither**.

4. **Check the product of the slopes**:
- The first slope is **1/4**, and the second slope is **-4**.
- Multiply them together: \( (1/4) * (-4) = -1 \).

Since the product of the slopes is **-1**, the two lines are **perpendicular**.