Which of the following equation represents a line parallel to y axis

Options

A. 2x=3y
B. 2y=4
C. 2x=4
D. 2x-3y=9

Answer

To determine which of the given equations represents a line that is parallel to the y-axis, we need to analyze the equations provided in the options. A line parallel to the y-axis can be expressed in the form \( x = a \), where \( a \) is a constant. This means that the line does not change in the x-direction and remains vertical.

Let's go through the options step by step:

### Step 1: Analyze the first equation \( 2x = 3y \)

1. Rearranging the equation to express y in terms of x:
\[ 3y = 2x \implies y = \frac{2}{3}x \]
2. This equation represents a line with a slope of \(\frac{2}{3}\), which means it is not parallel to the y-axis.

**Hint:** A line parallel to the y-axis will not have a term involving y when rearranged.

### Step 2: Analyze the second equation \( 2y = 4 \)

1. Rearranging the equation to express y:
\[ y = \frac{4}{2} = 2 \]
2. This equation represents a horizontal line at \( y = 2 \), which is not parallel to the y-axis.

**Hint:** A horizontal line has a constant y-value and varies in x, hence it is not parallel to the y-axis.

### Step 3: Analyze the third equation \( 2x = 4 \)

1. Rearranging the equation to express x:
\[ x = \frac{4}{2} = 2 \]
2. This equation is in the form \( x = a \), where \( a = 2 \). This represents a vertical line that is parallel to the y-axis.

**Hint:** Look for equations that can be simplified to the form \( x = a \) to identify lines parallel to the y-axis.

### Conclusion

Based on the analysis of the three equations, the equation that represents a line parallel to the y-axis is:

**Answer:** \( 2x = 4 \) (Option C)