The sample space is: (1, 1); (1, 2) - sum of 3; (1, 3); (1, 4); (1, 5) - sum of 6; (1, 6); (2, 1) - sum of 3; (2, 2); (2, 3); (2, 4) - sum of 6; (2, 5); (2, 6); (3, 1); (3, 2); (3, 3) - sum of 6; (3, 4); (3, 5); (3, 6) - sum of 9; (4, 1); (4, 2) - sum of 6; (4, 3); (4, 4); (4, 5) - sum of 9; (4, 6); (5, 1) - sum of 6; (5, 2); (5, 3); (5, 4) - sum of 9; (5, 5); (5, 6); (6, 1): (6, 2); (6, 3) - sum of 9; (6, 4); (6, 5); (6, 6)
Parallel lines have equal slopes, but different y intercepts. So the answer will be in the form y = 2x+c, where b and c are different numbers. Since b = 5, this means c must be some other number. If c = 5, then we'd have the exact same line.
Let's plug in (x,y) = (-5,12), along with the slope m = 2, and solve for c
y = mx+c
12 = 2(-5)+c
12 = -10+c
12+10 = c
22 = c
c = 22
Since m = 2 and c = 22, we go from y = mx+c to y = 2x+22