Are the lines parallel, perpendicular, or neither?

5x+2y=10

15x+4y = - 4

These lines are neither

Rearrange the lines by solving for y:

(-5x+10) / 2, so this line has a slope of - 2.5

(-15x-4) / 4, so this lines has a slope of - 3.75

For lines to be parallel, they must have the same slope which is clearly not the case here.

For lines to be perpendicular, they must be negative reciprocals of each other. In this case they are both negative slopes, so they are not perpendicular either.

So these lines are neither.