Question

Line m passes through the points (4, 1) and (7, 3) while line n passes through the points (-3, 5) and (-9, 1). Which statement accurately describes the relationship between the two lines?
A. Lines m and n have opposite reciprocal slopes so they are perpendicular.
B. Lines m and n have the same slope so they are perpendicular.
C. Lines m and n have the same slope so they are parallel.
D. Lines m and n have opposite reciprocal slopes so they are parallel.

Answer 1

Answer: C. Lines m and n have the same slope so they are parallel.

Step-by-step explanation:

We know that the the slope(m) of a line passing through points (a,b) and (c,d) is $p=\frac{d-b}{c-a}$

Thus, the slope of line m passes through the points (4, 1) and (7, 3) will be

$m_1=\frac{3-1}{7-4}=\frac{2}{3}$

The slope of line n passes through the points (-3, 5) and (-9, 1) will be

$m_2=\frac{1-5}{-9-(-3)}=\frac{-4}{-6}=\frac{2}{3}\\\Rightarrow\ m_2=\frac{2}{3}=m_1$

Therefore, Lines m and n have the same slope and if slopes of two lines are same then they are parallel.

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

Answer 2

The correct answer is C. Lines m and n have the same slope so they are parallel. The slope = 2/3