The graph of the linear equation 4x=6 is parallel to which axis

Answer

To determine which axis the graph of the linear equation \(4x = 6\) is parallel to, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Equation**: Start with the given equation:
\[ 4x = 6 \]

2. **Isolate \(x\)**: To find the value of \(x\), divide both sides of the equation by 4:
\[ x = \frac{6}{4} \]

3. **Simplify the Fraction**: Simplify \(\frac{6}{4}\):
\[ x = \frac{3}{2} \]

4. **Interpret the Result**: The equation \(x = \frac{3}{2}\) indicates that \(x\) is always \(\frac{3}{2}\) regardless of the value of \(y\). This means that for any value of \(y\), \(x\) will remain constant.

5. **Determine Parallelism**: Since the value of \(x\) does not change with varying \(y\), the graph of this equation is a vertical line. Vertical lines are parallel to the **y-axis**.

### Conclusion:
The graph of the linear equation \(4x = 6\) is parallel to the **y-axis**.