Determine whether the pair of lines is parallel, perpendicular, or neither.3x - 4y = -38x + 6y = -3

To determine whether the pair of lines is parallel, perpendicular, or neither, we first need to find the slopes of the two lines.

The equation of a line is generally given in the form y = mx + c, where m is the slope.

So, let's convert the given equations into this form:

1. 3x - 4y = -3 -4y = -3x -3 y = (3/4)x + 3/4

So, the slope (m1) of the first line is 3/4.

2. 8x + 6y = -3 6y = -8x -3 y = -(4/3)x - 1/2

So, the slope (m2) of the second line is -4/3.

If the lines were parallel, their slopes would be equal. But m1 is not equal to m2, so the lines are not parallel.

If the lines were perpendicular, the slopes would be negative reciprocals of each other. This means that m1 * m2 = -1. But (3/4) * (-4/3) = -1, so the lines are perpendicular.

Therefore, the pair of lines is perpendicular.