please please help me i have been stuck for hours

Question

Identify the graph of the linear equation 4x + 2y + z = 8 in three dimensional space.

A.)

B.)

C.)

D.)



Please just give explanation and solution.

Answer 1

Just try the points out.

Answer a) has the points (x, y, z) as Point1: (0,0,8), Point 2: (2,0,0), and Point 3:(0,4,0)

Plugging these into the equation we get:

4x + 2y + z = 8

Point 1: 4(0) + 2(0) + (8) = 8 which gives 8 = 8 (a true statement)

Point 2: 4(2) + 2(0) + (0) = 8 which gives 8 = 8 (a true statement)

Point 3: 4(0) + 2(4) + (0) = 8 which gives 8 = 8 (a true statement)

So it looks like answer a) is correct.

Take a look at the other answers and you will see they give false results (Example, answer b) lists a point (0,0,2) which plugged in gives 4(0) + 2(0) + (2) = 8 which gives 2 = 8 (a false statement).

Answer 2

Take the three points and plug into equation.

If any point doesn't work, then that choice is not it.