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

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

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

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

Answer 1

Find the slope of Line A: m = (13 − 5)/(6 − 2) = 8/4 = 2. Line B has slope 2 (y = 2x + 7). Since both slopes are equal but the y-intercepts (1 for Line A, 7 for Line B) are different, the lines are distinct and parallel.

Answer: D.