Question

Line A passes through the points (2,5) and (6,13). Line B is represented by the equation y=2x+7. Which statement best describes the relationship between Line A and Line B? Explain your reasoning

A.
The lines are the same line because they have the same slope and y-intercept.

B.
The lines are neither parallel nor perpendicular because their slopes are different but not negative reciprocals.

C.
The lines are perpendicular because their slopes are negative reciprocals.

D.
The lines are parallel because they have the same slope.

Answer 1

D. The slope of Line A is (13−5)/(6−2) = 2, and Line B has slope 2 (from y = 2x + 7). Since they have the same slope but different y-intercepts (Line A has y-intercept 1, Line B has 7), the lines are parallel.