Are the lines with equations 2x + y = 2 and x - 2y = 0 parallel, perpendicular or neither?

If the lines are perpendicular, then the product of their slopes
is -1.

For the beginning, we'll verify if the lines are
intercepting. For this rason, we'll solve the system

 2x + y = 2
(1)

x - 2y = 0 => x = 2y
(2)

We'll substitute (2) in (1):

4y + y
= 2

5y = 2

y =
2/5

x = 2*y

x =
4/5

The intercepting point is (4/5 ;
2/5).

Now, we'll write the equation in the standard
form:

y = mx + n, where m is the slope and n is the y
intercept.

 2x + y = 2

We'll isolate y
to the left side:

y = -2x + 2

The slope
m1 = -2.

We'll put the 2nd equation in the standard
form:

x = 2y

y =
x/2

m2 = 1/2

Now, we'll verify if the
product of the slopes gives -1:

m1*m2 =
-1

-2*1/2 = -1

-1 =
-1

Since the product is -1, the lines
are perpendicular.