SOLUTION: Find an equation of the plane that passes through the points (−1, 0, −4),(2, 1, 8),and (−1, 1, −1).(Suggestion: The equation of a plane can be written as

z = ax + by + c

Substitute (x, y, z) = (-1, 0, -4)

        -4 = a(-1) + b(0) + c

        -4 = -a + c

     a - c = 4

Substitute (x, y, z) = (2, 1, 8)

          8 = a(2) + b(1) + c

          8 = 2a + b + c

-2a - b - c = -8

 2a + b + c = 8

Substitute (x, y, z) = (-1, 1, -1)

        -1 = a(-1) + b(1) + c

        -1 = -a + b + c

 a - b - c = 1


So we have this system of equations:



That's easy to solve for a, b, and c.

The substitute the vales you get for a,b, and c

in z = ax + by + c to get your answer.

Want to see your plane graphed in 3D?  Look below.

It's the plane in which the green triangle is in. 





Edwin