Determine a if the lines are parallel: x+y=1 and 3x-ay=2

To determine if x+y =1 and 3x-3ay =2 are
parallel.

Two lines  are parallel if they have the same
slope.

We know that the the equation of any line in the
slope intercept form is y = mx+c, wher m is the slope.

So
we convert the given  lines into the slope intercept form as
below;

x+y = 1.

Subtract x
:

y = -x+1 which has a slope
-1......(1).

So y = -x+1 is the slope intercept form of x+y
= 1.

Consider the second  line 3x-ay =2. Subtract 3x from
both sides:

-ay = -3x
+2.

Divide by -a.

y = -3x/(-a)
+2/(-a)

y = (3/a)x 
+(-2/a)...........(2)

This line has a slope of 
3/a.

If  the two line are parallel , the their slopes
should be equal;

Therefore from (1) and
(2),

3/a = -1

Multiply by
a:

3 = -a. Or

So if  a = -3 ,
then the given two lines would be parallel.

a =
-3.