The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither.
a)m=2/3,m=4/6
b)m=3/4,m=-4/3
c)m=2,m=-2
d)m=1,m=-1
e)m=1/5,m=0.2
f)m=2 1/4, m=-4/9
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
a) Let's find the slopes of the two lines:
Line 1: m = 2/3
Line 2: m = 4/6
The slopes are both equal to 2/3, so the lines are parallel.
b) Let's find the slopes of the two lines:
Line 1: m = 3/4
Line 2: m = -4/3
The slopes are negative reciprocals of each other, (-4/3 = -3/4), so the lines are perpendicular.
c) Let's find the slopes of the two lines:
Line 1: m = 2
Line 2: m = -2
The slopes are negative reciprocals of each other, (-2 = -1/2), so the lines are perpendicular.
d) Let's find the slopes of the two lines:
Line 1: m = 1
Line 2: m = -1
The slopes are negative reciprocals of each other, (-1 = -1/1), so the lines are perpendicular.
e) Let's find the slopes of the two lines:
Line 1: m = 1/5
Line 2: m = 0.2
The slopes are equal to each other, but not negative reciprocals, so the lines are neither parallel nor perpendicular.
f) Let's find the slopes of the two lines:
Line 1: m = 2 1/4 = 9/4
Line 2: m = -4/9
The slopes are neither equal nor negative reciprocals of each other, so the lines are neither parallel nor perpendicular.
In conclusion:
a) The lines are parallel.
b) The lines are perpendicular.
c) The lines are perpendicular.
d) The lines are perpendicular.
e) The lines are neither parallel nor perpendicular.
f) The lines are neither parallel nor perpendicular.