Question

Indicate whether the lines are parallel, perpendicular, or neither. Justify your answer. a) y=5/2x−3 and 2y=−5x−4

a) Parallel, slopes are equal
b) Perpendicular, slopes are negative reciprocals
c) Neither, slopes are different
d) Neither, slopes are equal

Answer 1

The first line has a slope of 5/2 while the second line, when converted to slope-intercept form, has a slope of -5/2. Since these slopes are negative reciprocals of each other, the lines are perpendicular.

Step-by-step explanation:

To determine if the lines represented by the equations y=5/2x−3 and 2y=−5x−4 are parallel, perpendicular, or neither, we must first express both equations in slope-intercept form (y=mx+b), where m represents the slope and b represents the y-intercept.

The first equation is already in slope-intercept form with a slope of 5/2. To convert the second equation to slope-intercept form, we divide everything by 2, yielding y=−5/2x−2. This equation has a slope of −5/2.

Since the slopes of both lines are negative reciprocals of each other (−5/2 is the negative reciprocal of 5/2), we can conclude that the lines are perpendicular to each other. Therefore, the correct answer is (b) Perpendicular, slopes are negative reciprocals.