How to find unkown value for slopes of parallel segments and slopes of perpendicular line segments??

Question

How to find unknown value of slopes for parallel segments and slopes of perpendicular line segments?

For example, -K/3, 1/5 (Parallel slope), K/7, -3/2 (Perpendicular line segments)


What are the steps and rules to do this so that I can do it on my own????

Answer 1

I think the way it works is that for paralell slopes the slopes must be equal. So for the example you provide, you set the two slopes equal to eachother and solve for K:

-K/3 = 1/5
*multiply by -3 to both sides
K = -3/5

Knowing K, plug it back in, and youfind that the slope (-K/3) is equal to 1/5 - how to double check.

For perpendicular line segments in order for two lines to be perpendicular, they must have equal but opposite slopes. So if one line has a slope of -1 the other must have a slope of 1. In other words:

Slope A = - Slope B

So substituting K/7 for A and -3/2 for B:

K/7 = 3/2 (the negatuves cancelled out)
*multiply both sides by 7
K = 7 * 3/2 = 21/2

Plug this value of K back into the K/7 and you find the slope is 3/2 - opposite of -3/2! The only time this wont work is if one of the slopes is 0 - then the other slope must be infinity (since no negative 0) which just means a straight vertical line.

Answer 2

Parallel: The slopes have the same value

Perpendicular: The product of the slopes is -1.

-K/3, 1/5 (Parallel slope) => -K/3 = 1/5
K = -3/5

K/7, -3/2 (Perpendicular line segments) => K/7*(-3/2) = -1
3K/14 = 1
K = 14/3

Answer 3

If two lines are perpendicular, their slopes are negative reciprocals.

Parallel lines have the same slope.