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
nor equivatent
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope (m) of a line indicates how steep the line is and is calculated as the change in y divided by the change in x (rise over run).
A) m = 3/4 and m = 12/16:
First, we simplify both fractions:
m = 3/4 = 12/16
Since the slopes are equal, the lines are parallel. The lines have the same steepness or inclination.
B) m = 100 and m = 0.01:
In this case, the slopes are not equal, so the lines are not parallel.
To determine perpendicularity, we need to check if the slopes are negative reciprocals of each other. This means that if one slope is the reciprocal of another, it should have the opposite sign.
C) m = 10 and m = -0.1:
To check for perpendicularity, we find the reciprocal of the second slope and change its sign:
m = 10 and reciprocal of -0.1 = -1/(-0.1) = 1/0.1 = 10
Since the slopes are negative reciprocals of each other, the lines are perpendicular.
Overall, to determine whether lines are parallel, perpendicular, or neither, compare their slopes. If the slopes are equal, the lines are parallel. If the slopes have opposite signs and are reciprocals of each other, the lines are perpendicular. If the slopes are neither equal nor reciprocals, then the lines are neither parallel nor perpendicular.