Answer:
x + y - 5z = 52
Step-by-step explanation:
Given data:
Point on the plane (3,4,-9)
parallel to x + y -5z = 1
Finding the normal vector
(1 , 1 , -5)(x, y , z) = 1
the normal vector is (1 , 1 , -5)
formula for finding equation the plane given the normal vector (a,b,c) and point (m,n,o) is as
a(x - m) + b(y - n) + c(z-o)=0
Substituting the data we have
1(x-3) + 1( y- 4) - 5(z+9) =0
x-3 +y -4 -5z -45 = 0
x + y - 5z = 45 +4 +3
x + y - 5z = 52
