Determine if the lines are parallel, perpendicular, or neither 10x+5y=-5 and y=-2x+6

If they are parallel they will have the same slope, m

So in y = mx + c, if there are two equations which both have the same m value they will be parallel.

If the lines are perpendicular they'll have slopes like this: 1/2 to - 2/1 - where they flip and a negative gets added.

In the equations: 10x + 5y = - 5, and y = - 2x + 6

We can rearrange 10x + 5y = - 5 to be in the form y = mx + c

10x + 5y = - 5

5y = - 5 - 10x

y = - 1 - 2x

y = - 2x - 1

Since y = - 2x - 1 and y = - 2x + 6 both have the same slope of - 2 they are parallel!