https://file.aiquickdraw.com/mathbot/file/1730418193576wvsuzi93.jpg

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?

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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.

Match the equations to the coordinate planes as shown in the provided image.

Understand how to match equations to their corresponding coordinate planes in 3D space. Learn about plane equations such as x = 0, y = 0, and z = 0, and how these equations define the XY, YZ, and XZ planes. Suitable for students in Grades 9-12 studying coordinate geometry.

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