If ax + 6y = 4 , 3x + by = 1 and 5x + 3y = 8 are parallel lines, what are a and b equal to?

If ax + 6y = 4 , 3x + by = 1 and 5x + 3y = 8 are parallel
lines, what are a and b equal to?

We write both lines in
the  slope intercept form like y = mx+c, where m is the slope and c  is the the y
intercept of the line y = mx+c.

ax+6y =
4.

We subtract ax from both
sides.

6y = 4-ax.

We divide
both sides by 6

y = (4-ax)/6  =  (-a/6)x
+4/6.

So y =
-(a/6)x+2/3.....(1).

No
consider the line 3x+by = 1.

3x+by - 3ax =
1-3x

by = (1-3x).

by/b =
(1-3x)/b = -(3/b)x+1/b

y =
-(3/b)x+1/b..........(2).

Now
we consider the line 5x+3y = 8

=> 3y =
8-5x

=> y = (8-5x)/3 =
-(5/3)x+8.

=> y =
-(5/3)x+8.........(3)

Since
the (1) and (2) and (3) are parallel, their slopes -(a/6) ,  -(3/b)  and (-5/3) must be
equal.

=> -a/6 = -3/b =
-5/3.

=> a/6 = 5/3 = 10 and 3/b =
5/3

So a = 5*6/2 = 10 and b = 3*3/5  =
1.8

So a = 10 and b = 1.8.