Question

The slopes of 2 lines are in the attachment. what is the value of ‘a’ that will make the lines PARALLEL and PERPENDICULAR

Answer 1

a. a = -12

b. a = 27

Explanation:

a. Two lines that are parallel have the same slope, making the slopes equal ot each other:

`-(3)/(2) =(18)/(a)`

We can cross multiply and solve for a:

`-3a = 36\\a = -12`

b. Two lines that are perpendicular have the negative reciprocal of each other. This means that you would flip the fraction and multiply by a negative as shown below:

`-(3)/(2) --> (2)/(3)`

This would be the slope of the other line, so we can write:

`(2)/(3) = (18)/(a)`

as both expressions express the slope of the same line. We can cross multiply and solve to get:

`2a = 54\\a = 27`