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The problem is asking to rotate the linear function \( y = x - 3 \) by \( 60^\circ \) around the origin (0,0). Let's solve it step by step.

### Step 1: Parametrize the line equation
The line \( y = x - 3 \) can be written as \( (x, y) = (x, x - 3) \). We will rotate the points on this line around the origin.

### Step 2: Rotation matrix
The general formula for rotating a point \( (x, y) \) by an angle \( \theta \) counterclockwise around the origin is given by the rotation matrix:
\[
\begin{pmatrix}
x' \\
y'
\end{pmatrix}
=
\begin{pmatrix}
\cos\theta & -\sin\theta \\
\sin\theta & \cos\theta
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
\]
For \( \theta = 60^\circ \), the values are \( \cos 60^\circ = \frac{1}{2} \) and \( \sin 60^\circ = \frac{\sqrt{3}}{2} \).

### Step 3: Apply the rotation
Substituting these values, the rotation matrix becomes:
\[
\begin{pmatrix}
x' \\
y'
\end{pmatrix}
=
\begin{pmatrix}
\frac{1}{2} & -\frac{\sqrt{3}}{2} \\
\frac{\sqrt{3}}{2} & \frac{1}{2}
\end{pmatrix}
\begin{pmatrix}
x \\
x - 3
\end{pmatrix}
\]
Now, perform the matrix multiplication to get the new coordinates \( (x', y') \).

### Step 4: Simplify the new equation
Performing the matrix multiplication:
\[
x' = \frac{1}{2}x - \frac{\sqrt{3}}{2}(x - 3) = \frac{1}{2}x - \frac{\sqrt{3}}{2}x + \frac{3\sqrt{3}}{2}
\]
\[
y' = \frac{\sqrt{3}}{2}x + \frac{1}{2}(x - 3) = \frac{\sqrt{3}}{2}x + \frac{1}{2}x - \frac{3}{2}
\]
Now simplify these equations:
\[
x' = \left(\frac{1 - \sqrt{3}}{2}\right)x + \frac{3\sqrt{3}}{2}
\]
\[
y' = \left(\frac{\sqrt{3} + 1}{2}\right)x - \frac{3}{2}
\]

This gives the parametric form of the line after rotation.

Let me know if you'd like further details or clarifications on this process.

### Related questions:
1. How would you rotate the function if the angle were \(90^\circ\) instead of \(60^\circ\)?
2. How can you express a general transformation of a linear function using matrices?
3. What is the geometric significance of rotating a line around the origin?
4. How would this process change if the line were rotated about a different point?
5. Can you find the intersection point of the original and rotated lines?

### Tip:
When rotating a line, always use parametric equations for the original line to make the matrix multiplication straightforward.

Fungsi linear y = x - 3 dirotasikan 60° terhadap titik nol. Bayangan fungsi linear tersebut adalah...

Explore how to rotate the linear function y = x - 3 by 60° counterclockwise around the origin. Learn about the transformation matrix and how to apply it to find the new coordinates.

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