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The given problem asks for the transformation of the linear function \( y = x + 7 \) when it is rotated clockwise by \( 90^\circ \) about the origin.

### Step-by-step solution:

1. **Original Line Equation**: The line equation is \( y = x + 7 \). In slope-intercept form, the slope \( m \) of this line is 1 (since \( y = mx + c \), where \( m = 1 \) and \( c = 7 \)).

2. **Clockwise Rotation by \( 90^\circ \)**: 
   - When a line with slope \( m \) is rotated by \( 90^\circ \) clockwise about the origin, its new slope becomes the negative reciprocal of \( m \), i.e., \( m_{\text{new}} = -\frac{1}{m} \). 
   - In this case, since \( m = 1 \), the new slope after a \( 90^\circ \) clockwise rotation will be \( m_{\text{new}} = -1 \).

3. **New Line Equation**: 
   - The new equation of the line will have the form \( y = -x + c \). To find \( c \), the line must pass through the same point on the original line that was rotated.
   - The line intersects the y-axis at \( (0, 7) \). After rotating this point \( 90^\circ \) clockwise, the new coordinates of the point are \( (7, 0) \).

4. **Final Equation**:
   - Using the point \( (7, 0) \), substitute it into the new equation \( y = -x + c \):
     \[
     0 = -7 + c \implies c = 7
     \]
   - Thus, the new equation of the line is \( y = -x + 7 \).

### Conclusion:
The equation of the line after a \( 90^\circ \) clockwise rotation is \( y = -x + 7 \).

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Would you like more details or have any questions?

Here are five related questions to explore further:

1. What happens when the line is rotated \( 90^\circ \) counterclockwise instead?
2. How do you rotate a line around a different point other than the origin?
3. What is the geometric meaning of rotating a line about the origin?
4. How would the transformation change if the rotation angle were \( 180^\circ \)?
5. Can you rotate other types of curves, like parabolas, in the same way?

**Tip**: Rotating lines involves changing their slope, but always remember that rotations around the origin also involve changing the coordinates of points on the line!

Fungsi linear y = x + 7 dirotasikan searah jarum jam sebesar 90 derajat terhadap titik pusat. Bayangan dari fungsi linear tersebut adalah...

This problem demonstrates how to rotate the linear function y = x + 7 by 90 degrees clockwise around the origin. It involves key concepts in linear equations and geometric transformations. Suitable for students in Grades 9-10.

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