To solve this problem, let’s identify each coordinate plane in 3D space and match it with the equations given.

Coordinate Plane Analysis

1. Plane $y = 0$: This is the YZ-plane because $y = 0$ means the $y$-coordinate is fixed at zero, allowing only $x$-variation.
2. Plane $z = 0$: This is the XY-plane because $z = 0$ fixes the $z$-coordinate at zero, allowing only $x$- and $y$-coordinates to vary.
3. Plane $x = 0$: This is the XZ-plane because $x = 0$ fixes the $x$-coordinate at zero, allowing only $y$- and $z$-coordinates to vary.

Matching Equations to Figures

Looking at the provided figures:

• Figure (a): This is a vertical plane oriented along the $y$-axis, so this matches with $y = 0$ (the YZ-plane).
• Figure (b): This is also a vertical plane, but oriented along the $x$-axis, which matches with $x = 0$ (the XZ-plane).
• Figure (c): This is a horizontal plane at the base, which corresponds to $z = 0$ (the XY-plane).

Final Matching

• (a): $y = 0$
• (b): $x = 0$
• (c): $z = 0$

Would you like a detailed explanation or have any questions?

Here are five related questions to deepen your understanding:

1. What would the equation $y = 5$ represent in 3D space?
2. How do the coordinate planes help in visualizing functions of multiple variables?
3. How would you describe the plane $x = 3$ in terms of geometry?
4. Can a plane be represented by more than one equation?
5. How does changing the value in equations like $x = 0$ affect the location of the plane?

Tip: Visualizing the 3D coordinate planes in terms of which axis they "cut" through helps in understanding their equations.