Decide if the lines in each pair are parallel, perpendicular, or neither, and justify your answers. The slopes of the lines are given.
a) m=3/4 and m=12/16
b) m=10 and m = -0.1
To determine if two lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.
a) For the first pair of lines:
m₁ = 3/4 and m₂ = 12/16
To compare these slopes, we can simplify them both:
m₁ = 3/4
m₂ = 3/4
Since the slopes are the same, m₁ = m₂ = 3/4, the lines are parallel. Two lines with the same slope are always parallel.
b) For the second pair of lines:
m₁ = 10 and m₂ = -0.1
Comparing the slopes, we can see that they are not the same. However, the slopes are negative reciprocals of each other. To confirm if the lines are perpendicular, we can multiply the slopes together and check if the result is -1.
m₁ * m₂ = 10 * (-0.1) = -1
Since the product of the slopes is -1, the lines are perpendicular. Two lines with slopes that are negative reciprocals of each other are always perpendicular.
In summary:
a) The lines with slopes 3/4 and 12/16 are parallel.
b) The lines with slopes 10 and -0.1 are perpendicular.
slopes the same: parallel
slopes multiply to -1: perpendicular
otherwise, neither