Question

is the point (1, 4, 2) or the point (2, 2, -6) on the graph of 3x -2y +z + 4 =0

Answer 1

Equation: 3X - 2Y + Z + 4 = 0

Points to Check: (1, 4, 2) & (2, 2, -6)

Simply plug in the values to see if they work!

Plug in (1, 4, 2) to get 3(1) - 2(4) + (2) + 4 = 0
And simplify.
3 - 8 + 2 + 4 = 0
-5 + 2 + 4 = 0
-3 + 4 = 0
-1 = 0

^^ That does not work, so the point (1, 4, 2) does not lie on the original function.

Now plug in (2, 2, -6) to get 3(2) - 2(2) + (-6) + 4 = 0
And simplify.
6 - 4 - 6 + 4 = 0
You may already see how this will all cancel out.
2 - 6 + 4 = 0
-4 + 4 = 0
0 = 0

^^ That does work, so the point (2, 2, -6) lies on the original function.