Decide whether the lines in each pair are parallel , perpendicular, or neither. Justify your answers:

A.) m=3/4 m=12/16
B.) m=100 m=0.01
C.) m=10 m= -0.1

My answers:
A.) parallel because they both equal to 0.75
B.) neither because they aren't the same and aren't negative recipricales
C.) perpendicular because they r negative recipricales

To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope, denoted as 'm,' indicates the rate of change of the line.

Given the slopes for each pair of lines, let's analyze them:

A.) m = 3/4, m = 12/16
To simplify the slopes, we reduce them to the simplest form:
3/4 = 12/16 = 3/4

Since the slopes are equal, the lines are parallel. This is because parallel lines have the same slope.

B.) m = 100, m = 0.01
The slopes are clearly different and not negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

C.) m = 10, m = -0.1
To determine if the slopes are negative reciprocals, we invert the second slope and change its sign:
-0.1 -> 1/(-0.1) = -10

The two slopes are negative reciprocals of each other (-10 and 10), which means the lines are perpendicular. This is a property of perpendicular lines - their slopes are negative reciprocals of each other.

Therefore, to summarize the answers:

A.) The lines are parallel.
B.) The lines are neither parallel nor perpendicular.
C.) The lines are perpendicular.