The graph of y =x passes through the point

Options

A. `(5/2,-5/2)`
B. `(0,5/2)`
C. `(1,1)`
D. `(-1/2,1/2)`

Answer

To determine which points lie on the graph of the equation \( y = x \), we will check each given point by substituting its coordinates into the equation. If the left-hand side (LHS) equals the right-hand side (RHS), then the point lies on the graph.

### Step-by-Step Solution:

1. **Identify the Equation**:
The equation given is \( y = x \).

2. **Check the First Point \( \left(\frac{5}{2}, -\frac{5}{2}\right) \)**:
- Substitute \( x = \frac{5}{2} \) and \( y = -\frac{5}{2} \) into the equation.
- LHS: \( y = -\frac{5}{2} \)
- RHS: \( x = \frac{5}{2} \)
- Since \( -\frac{5}{2} \neq \frac{5}{2} \), this point does not lie on the graph.

3. **Check the Second Point \( (0, \frac{5}{2}) \)**:
- Substitute \( x = 0 \) and \( y = \frac{5}{2} \) into the equation.
- LHS: \( y = \frac{5}{2} \)
- RHS: \( x = 0 \)
- Since \( \frac{5}{2} \neq 0 \), this point does not lie on the graph.

4. **Check the Third Point \( (1, 1) \)**:
- Substitute \( x = 1 \) and \( y = 1 \) into the equation.
- LHS: \( y = 1 \)
- RHS: \( x = 1 \)
- Since \( 1 = 1 \), this point lies on the graph.

5. **Check the Fourth Point \( \left(-\frac{1}{2}, \frac{1}{2}\right) \)**:
- Substitute \( x = -\frac{1}{2} \) and \( y = \frac{1}{2} \) into the equation.
- LHS: \( y = \frac{1}{2} \)
- RHS: \( x = -\frac{1}{2} \)
- Since \( \frac{1}{2} \neq -\frac{1}{2} \), this point does not lie on the graph.

### Conclusion:
The only point that lies on the graph of the equation \( y = x \) is \( (1, 1) \).