y=1/4x-2

Question

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

Answer 1

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 2

break it down simplier without the extra symbols

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.