A point is on the y-axis. What equations in x,y,z are satified if & only if the point (x,y,z) is on the y-axis

Question

the topic here is space coordination(plotting in space with an x-axis, y-axis, and z-axis). my guess for this answer is 0x+y+0z=y, but i don't know if it is correct.

if my guess is right then would 0x+2y+0z=2d work? or 0x+212y+0z=212d and so on?

Answer 1

No, that is not correct.
It's x=0, z=0.

Compare it to the 2-dimensional situation: If a point is on the y axis, then x=0, and y can take any value at all.

In 3 dimensions, if the point is on the y axis, y can take any value at all. Picture the point as starting off at O, and moving to its current position. Only its y value has changed, x and z remain at 0.

Every equation stating or relating coordinates reduces the "degree of freedom", or "dimensions", by 1. With 3 coordinate axes, one linear equation reduces the 3-D space to a plane. To go down to a line (one dimension) we need two equations.

Thus 3x - 8y - 2z = 38 is the equation of a plane containing the points (4, -2, -5), (0, 1, -23), (10, -3, 8) and many more!!

2x - 4 = 15 - 3y = z - 1 are the equations defining a line through the points (2, 5, 1), (5, 3, 7), (-1, 7, -5) and many more.

Answer 2

you got it right
but you should write as the following:
0x+y+0z=D (not =y)