Question

question 12 of 40
line m passes through the points (5, 1) and (8, 6) while line n passes through the points (-4, 3) and (-1, 8).
which statement accurately describes the relationship between the two lines?
a. lines m and n have the same slope so they are parallel.
b. lines m and n have opposite reciprocal slopes so they are parallel.
c. lines m and n have opposite reciprocal slopes so they are perpendicular.
d. lines m and n have the same slope so they are perpendicular.

Explanation:

Step1: Calculate slope of line m

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For line m with points $(5,1)$ and $(8,6)$:
$m_m = \frac{6 - 1}{8 - 5} = \frac{5}{3}$

Step2: Calculate slope of line n

Using the same slope formula for line n with points $(-4,3)$ and $(-1,8)$:
$m_n = \frac{8 - 3}{-1 - (-4)} = \frac{5}{3}$

Step3: Compare slopes and identify relationship

Parallel lines have equal slopes; perpendicular lines have slopes that are opposite reciprocals. Here $m_m = m_n = \frac{5}{3}$, so the lines are parallel.

Answer:

A. Lines m and n have the same slope so they are parallel.