What is the relationship between ax+by = c and bx -ay = c if a,b,c are not zero?

Given the equations:

ax + by
= c

bx - ay = c

We notice that
the above are equations of two lines.

We need to find the
relation between the lines (i.e perpendicular, parallel, or
neither).

To determine the relations, we will rewrite the
equations into the slope form " y= mx + a) where m is the
slope.

==> ax + by =
c

==> by = -ax +
c

==> y (-a/b) x +
c/b...............(1)

Then slope for equation (1) is m1 =
-a/b.

Now we will rewrite the second
equation.

==> bx -ay =
c

==> -ay = -bx +
c

==> y= (b/a)x -
c/a..............(2)

The slope for equation (2) is m2=
b/a

Now we notice that m1 and m2 are NOT equal, then they
are not parallel.

However, m1*m2 = -a/b * b/a =
-1

Then, the relationship between the lines
is that they are perpendicular.