When graphing the following equation, where does the solution plane cross the z-axis?

3x – y + 4z = 32

Type your answer as an ordered triplet, like this: (-2, 14, 3)

Your plane is 3x-y+4z=32 and you want to know when it crosses the z-axis or in other words intersects it. Along the z axis only z changes, additionally it goes through the origin (0,0,0).
So we can insert x=y=0 into the plane to calculate the point along the z-axis where it intersects the plane:
3x-y+4z=32
insert 0s:
4z=32
z=8

so the solution plane intersects the z-axis at (0,0,8)

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When graphing the following equation, where does the solution plane cross the z-axis? 3x – y + 4z = 32 Type your answer as an ordered triplet, like this: (-2, 14, 3)

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When graphing the following equation, where does the solution plane cross the z-axis?

3x – y + 4z = 32

Type your answer as an ordered triplet, like this: (-2, 14, 3)