What is the solution set for 6x−9=15, given the replacement set {0, 1, 2, 3, 4}?

The answer is 4. plug it in the equation, 6(4) - 9 = 15
6 x 4 = 24, so 24 - 9 = 15

Try every single value, and a solution set means that the equation has to be true. So, if you plug in 0, you are left with -9 = 15. That doesn't satisfy the equation. If you plug in 1, you get -3 = 15, which is also not good. If you plug in 2, you get 12 - 9 = 3, which turns into 3 = 15, which doesn't satisfy it. Plug in 3, you get 6(3) - 9 = 9 = 15, which is not true. And finally try 4, 6(4) - 9 = 15. And, indeed, 24-9 = 15. 15 = 15 only if you plug in 4. So, that's your answer.

The linear equation is: y=ax+b