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

Answer:

a. a = -12

b. a = 27

Step-by-step explanation:

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

$-\frac{3}{2} =\frac{18}{a}$

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:

$-\frac{3}{2} --> \frac{2}{3}$

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

$\frac{2}{3} = \frac{18}{a}$

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

$2a = 54\\a = 27$