From where does the graph of the equation x - y = 0 passes?

Options

A. x - axis
B. y - axis
C. Origin
D. Data insufficient

Answer

To determine from where the graph of the equation \( x - y = 0 \) passes, we can follow these steps:

### Step 1: Rewrite the equation
The given equation is:
\[ x - y = 0 \]
This can be rewritten as:
\[ x = y \]
This means that for any value of \( x \), \( y \) will be equal to that value.

### Step 2: Find points on the graph
To find specific points on the graph, we can substitute different values for \( x \) and solve for \( y \).

1. **Substituting \( x = 0 \)**:
\[ x - y = 0 \implies 0 - y = 0 \implies y = 0 \]
So, one point is \( (0, 0) \).

2. **Substituting \( x = 1 \)**:
\[ x - y = 0 \implies 1 - y = 0 \implies y = 1 \]
So, another point is \( (1, 1) \).

3. **Substituting \( x = 2 \)**:
\[ x - y = 0 \implies 2 - y = 0 \implies y = 2 \]
So, another point is \( (2, 2) \).

### Step 3: Plot the points
Now we can plot the points we found on a Cartesian plane:
- Point \( (0, 0) \) is the origin.
- Point \( (1, 1) \) is one unit up and one unit right from the origin.
- Point \( (2, 2) \) is two units up and two units right from the origin.

### Step 4: Draw the graph
When we draw the graph using these points, we can see that they form a straight line. The line passes through the origin and continues in both directions.

### Conclusion
The graph of the equation \( x - y = 0 \) passes through the origin and the points \( (1, 1) \) and \( (2, 2) \).