Question

which statement best explains the relationship between lines pq and rs?
○ they are parallel because their slopes are equal.
○ they are parallel because their slopes are negative reciprocals.
○ they are not parallel because their slopes are not equal.
○ they are not parallel because their slopes are negative reciprocals.

Explanation:

Step1: Find coordinates of points for PQ

Point P: \((-5, 3)\), Point Q: \((5, 1)\). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Slope of PQ: \(m_{PQ} = \frac{1 - 3}{5 - (-5)} = \frac{-2}{10} = -\frac{1}{5}\).

Step2: Find coordinates of points for RS

Point R: \((-4, -2)\), Point S: \((0, -4)\).
Slope of RS: \(m_{RS} = \frac{-4 - (-2)}{0 - (-4)} = \frac{-2}{4} = -\frac{1}{2}\).

Step3: Compare slopes

Parallel lines have equal slopes. \(m_{PQ} = -\frac{1}{5}\), \(m_{RS} = -\frac{1}{2}\). Slopes are not equal, so lines are not parallel.

Answer:

They are not parallel because their slopes are not equal. (Third option: "They are not parallel because their slopes are not equal.")