An equation whose graph phasses through the origin, out of the form x = k where k is a constant, then graph of the eqation wil be

Options

A. ` 2 x - 3y = 3`
B. ` - 2 x + 3y = 5`
C. ` 2 x + 3y = 0 `
D. ` 2 x + 3y = 2 `

Answer

To solve the problem, we need to determine which equation of the form \( x = k \) passes through the origin (0, 0).

### Step-by-Step Solution:

1. **Understanding the Form of the Equation**:
The equation is given in the form \( x = k \), where \( k \) is a constant. This means for any value of \( y \), \( x \) will always equal \( k \).

2. **Identifying the Condition**:
For the graph to pass through the origin, the coordinates (0, 0) must satisfy the equation. Thus, we need to check if \( x = 0 \) can be satisfied by any constant \( k \).

3. **Substituting the Origin into the Equation**:
If we substitute \( x = 0 \) into the equation \( x = k \), we get:
\[ 0 = k \]
This means that the only value of \( k \) that satisfies this equation is \( k = 0 \).

4. **Conclusion**:
Therefore, the equation that passes through the origin is:
\[ x = 0 \]
This represents a vertical line along the y-axis.

5. **Verifying Other Cases**:
To ensure that no other equations of the form \( x = k \) can pass through the origin, we can consider other values of \( k \):
- If \( k = 1 \), then \( x = 1 \) does not pass through (0, 0).
- If \( k = 2 \), then \( x = 2 \) does not pass through (0, 0).
- If \( k = -1 \), then \( x = -1 \) does not pass through (0, 0).
- Only \( k = 0 \) satisfies the condition.

### Final Answer:
The graph of the equation that passes through the origin is:
\[ x = 0 \]