Find the value of y. The line containing (1,-3) and (3,y) is parallel to the line containing (5,-6) and (9,y).

Here, since the lines are parallel, they have the same slope....so.....we just need to equate slopes and solve for y.......and we have......

[y + 3 ] / [3 - 1 ]  =  [y + 6] / [9 - 5]         ...simplify....

[y + 3] / 2  = [y + 6] / 4                            ....cross-multiply...

4[y + 3 ] = 2 [ y + 6]

4y + 12 =  2y = 12             .... subtract 12 from both sides and 2y from both sides....

2y = 0                               ......divide by 2 on both sides.........

y = 0