Given: Plane passes through the points A(2, 3, 1) and B(4, -5, 3) and is parallel to x-axis

To find: Equation of plane

Formula Used: Equation of a plane parallel o x-axis is

b(y – y₁) + c(z – z₁) = 0

Explanation:

Let the equation of the plane be

b(y – y₁) + c(z – z₁) = 0

Since A(2, 3, 1) lies on the plane,

b(y – 3) + c(z – 1) = 0 … (1)

Since B(4, -5, 3) lies on the plane,

b(-5 – 3) + c(3 – 1) = 0

-8b + 2c = 0 or –4b + c = 0

b : c = 1 : 4

Substituting in (1),

y – 3 + 4z – 4 = 0

y + 4z = 7

The equation of the plane is y + 4z = 7