The slope of the new line must be - 3
Subtract 6x from both sides
2y + 6x - 6x = 15 - 6x
Collect like terms on the left
2y = 15 - 6x
Divide by 2
2y/2 = 15/2 - 6x/2
y = 7.5 - 3x
No matter how you represent it, the answer is the first equation on top. It's slope is -3
Problem Two
sqrt(x - 2) = x - 4 Square both sides
x - 2 = x^2 - 8x + 16 Switch sides
x^2 - 8x + 16 = x - 2 Subtract x from both sides.
x^2 - 8x - x + 16 = x - x - 2 Collect like terms on both sides.
x^2 - 9x + 16 = - 2 Add 2 to both sides
x^2 - 9x + 16 +2 = -2 + 2 Collect like terms
x^2 - 9x + 18 = 0 Factor
(x - 3)(x - 6) = 0
x- 3 = 0
x = 3
============
x - 6 = 0
x = 6
You have to be very careful with a question like this. Both answers have to checked: one of them may not work.
Let x = 3
sqrt(3 - 2) = 3- 4
sqrt (1) = - 1 This only works if you take the square root as +/- 1.
The minus root will wook
Let x = 6
sqrt(6 - 2) = x - 4
sqrt(4) = 6 - 4
2 = 2
x = 3 is kind of iffy.
x = 6 works.
I think I'd try 6 first. If the computer marks you wrong, you can include 3, but I don't think it is quite correct.
