Decide wheather the pairs of lines is parallel, perpendicular, or neither

4x+2y=6
2x-4y=4

Rewrite the equations in y = mx + b form.

The slope of the first line is -2 and the slope of the second line is +1/2

If the product of the two slopes is -1, the lines are perpendicular

Parallel

To determine whether the given pairs of lines are parallel, perpendicular, or neither, we can compare their slopes.

First, let's rewrite the given equations to the slope-intercept form (y = mx + b), where m represents the slope of each line:

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

2x - 4y = 4
-4y = -2x + 4
y = (-2/-4)x + 4/-4
y = (1/2)x - 1

Now, we can see that the slopes of the lines are -2 and 1/2, respectively.

If two lines have slopes that are negative reciprocals of each other, they are perpendicular. In this case, -2 * (1/2) = -1, so the lines are perpendicular.

Therefore, the given pairs of lines are perpendicular.