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The problem asks to reflect the function \( 6x - 2y = 4 \) over the line \( y = x \), and then to identify the correct graph of the reflected function.

### Steps:
1. **Rewrite the given equation**:
   \[
   6x - 2y = 4 \quad \text{or} \quad y = 3x - 2
   \]
   This is the equation of the line in slope-intercept form, where the slope is \(3\) and the y-intercept is \(-2\).

2. **Reflect the equation over \( y = x \)**:
   When reflecting over the line \( y = x \), we swap the variables \( x \) and \( y \). So, the reflection of the line \( y = 3x - 2 \) becomes:
   \[
   x = 3y - 2 \quad \text{or} \quad y = \frac{1}{3}x + \frac{2}{3}
   \]
   This new equation has a slope of \( \frac{1}{3} \) and a y-intercept of \( \frac{2}{3} \).

3. **Analyze the graphs**:
   We now need to identify which graph matches the reflected function \( y = \frac{1}{3}x + \frac{2}{3} \). This line has a positive slope of \( \frac{1}{3} \) and passes through \( y = \frac{2}{3} \) at \( x = 0 \).

   By examining the options, **Graph D** corresponds to the line with the correct slope and intercept.

### Final Answer:
The correct graph is **D**.

Would you like further clarification or details? Here are 5 related questions to deepen your understanding:

1. How do you reflect a function over the line \( y = -x \)?
2. What happens to the slope when reflecting a line over \( y = x \)?
3. Can you reflect a quadratic function over a line? If so, how?
4. What are the effects of reflecting over other lines like \( y = 0 \) or \( x = 0 \)?
5. How would you determine the reflection of a function in three dimensions?

**Tip:** When reflecting over \( y = x \), always swap \( x \) and \( y \) and then solve for \( y \) to get the new equation.

Jika fungsi 6x – 2y = 4 dicerminkan terhadap garis y = x, maka grafik bayangan fungsi tersebut adalah?

Solve the problem of reflecting the linear function 6x – 2y = 4 over the line y = x. This algebra problem covers key concepts of linear equations and reflections, suitable for Grades 10-12 students.

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