Are the following lines parallel, perpendicular, or neither?

3y=8x + 9

6x + 16y =32

First we have to convert the given equation of lines in slope intercept form i.e. in y = mx + c form

3y = 8x + 9

y = (8/3)x + (9/3)

y = (8/3) x + 3 ....................equation 1

slope of this line, m1 = 8/3

6x + 16y = 32

16y = -6x + 32

y = (-6/16)x + 32/16

y = (-3/8) x + 2 ........................equation 2

slope of this line, m2 = -3/8

m1 * m2 = (8/3) * (-3/8) = -1

As product of the slopes of two given line i.e. m1*m2 is -1, it means, given lines are perpendicular to each other.

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