https://file.aiquickdraw.com/mathbot/file/17304188529720pybyauy.jpg

To determine the equations of each plane, we analyze the position and orientation of each one with respect to the \( x \), \( y \), and \( z \) axes. Since each plane is parallel to a coordinate plane, each will have an equation where one of the variables is held constant.

### Solution:

**a) First Plane:**
- This plane is vertical and parallel to the \( yz \)-plane.
- The plane only intersects the \( x \)-axis, which means it has a constant \( x \)-value.
- Let’s assume the intersection is at \( x = a \) (based on the image, it appears to intersect at \( x = 3 \)).

**Equation for (a):**  
\[
x = 3
\]

**b) Second Plane:**
- This plane is horizontal and parallel to the \( xy \)-plane.
- The plane intersects the \( z \)-axis at a specific height, so it has a constant \( z \)-value.
- Based on the image, it looks like \( z = 2 \).

**Equation for (b):**  
\[
z = 2
\]

**c) Third Plane:**
- This plane is vertical and parallel to the \( xz \)-plane.
- The plane intersects the \( y \)-axis, indicating a constant \( y \)-value.
- Observing the image, the intersection appears to be at \( y = -1 \).

**Equation for (c):**  
\[
y = -1
\]

### Summary of Answers:
1. **(a)** \( x = 3 \)
2. **(b)** \( z = 2 \)
3. **(c)** \( y = -1 \)

Would you like further explanations on these solutions or have any specific questions?

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Here are five additional related questions for practice:

1. How would you find the equation of a plane if it were parallel to both the \( xz \)-plane and passed through \( y = 5 \)?
2. What is the general form of a plane that is parallel to the \( xy \)-plane and passes through a given \( z \)-value?
3. If a plane intersects both the \( x \)-axis and the \( z \)-axis, but is parallel to the \( yz \)-plane, how would you determine its equation?
4. How can you determine if a given point lies on one of these planes?
5. What would the equation be if a plane is parallel to the \( x \)-axis and passes through \( y = -2 \) and \( z = 4 \)?

**Tip:** When determining the equation of a plane that is parallel to one of the coordinate planes, identify the axis that the plane does not depend on, and set the constant value for the axis it intersects.

Enter the equation for each plane based on its orientation with respect to the coordinate axes. Each plane is parallel to one of the coordinate planes.

Learn how to determine the equations of planes in 3D space that are parallel to one of the coordinate planes. This problem focuses on recognizing the constant values of x, y, or z for each plane and is suitable for students in Grades 10-12.

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