Are the pairs of lines parallel, perpendicular, or neither? Explain

a. 3xx + 2yy = 74 and 9xx - 6yy = 15

b. 4xx - 9yy = 8 and 18xx + 8yy = 7

a) neither perpendicular nor parallel

b) perpendicular

Step-by-step explanation:

a)

3x + 2y = 74

Lets put y in function of x

2y = 74-3x

y = 37 - 1.5 x

On the other hand

9x - 6y = 15

-6y = 15 - 9x

y = - 2.5 + 1.5 x

The lines are not parallel because if that is the case, then their slope should be equal, but one slope is 1.5 and the other is - 1.5.

If 2 lines are perpendicular, then the product of their slopes should be equal to - 1, however 1.5 * - 1.5 = - 2.25, which is different from - 1. Thus, the lines are neither perpendicular nor parallel.

b) 4x - 9y = 8

-9y = 8 - 4x

y = 8/9 + 4/9 x

On the other hand

18x+8y = 7

8y = 7 - 18x

y = 7/8 - 9/4 x

The slopes are different, so the lines arent parallel, but they are perpendicular, because

4/9 * (-9/4) = - 1