Question

select whether the pair of lines is parallel, perpendicular, or neither.

Explanation:

Step1: Recall line - relationship rules

Parallel lines have equal slopes, and perpendicular lines have slopes that are negative reciprocals.

Step2: Find the slope of a line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's assume two points on one line are $(x_1,y_1)$ and $(x_2,y_2)$ and on the other line are $(x_3,y_3)$ and $(x_4,y_4)$.
For the first line, if we take two points (say $P$ and $Q$), and for the second line, if we take two points (say $T$ and $U$). By counting the rise - over - run on the grid:
Let's assume for the first line passing through two points, if the rise is $- 2$ and the run is $2$, the slope $m_1=\frac{-2}{2}=-1$.
For the second line, if we take two appropriate points and count the rise and run, if the rise is $-2$ and the run is $2$, the slope $m_2 = \frac{-2}{2}=-1$.
Since $m_1 = m_2=-1$, the two lines are parallel.

Answer:

Parallel