Question

parallel, perpendicular, or neither.
$y = -\frac{1}{4}x + 2$
$x + 4y = -8$
circle one:
parallel perpendicular neither
explain your answer:

Explanation:

Step1: Find the slope of the second line

We transform the equation \(x + 4y=-8\) into slope - intercept form \(y = mx + b\) (where \(m\) is the slope).
Subtract \(x\) from both sides: \(4y=-x - 8\).
Divide each term by \(4\): \(y=-\frac{1}{4}x-2\).
The slope of the second line \(m_2 =-\frac{1}{4}\).

Step2: Compare the slopes

The first line is \(y =-\frac{1}{4}x + 2\), its slope \(m_1=-\frac{1}{4}\).
Since \(m_1 = m_2=-\frac{1}{4}\), the two lines are parallel.

Answer:

Parallel.
Because the slopes of the two lines \(y =-\frac{1}{4}x + 2\) and \(y=-\frac{1}{4}x-2\) are equal (\(m_1 = m_2=-\frac{1}{4}\)), according to the property of parallel lines (if two lines have the same slope, they are parallel), the two lines are parallel.