https://file.aiquickdraw.com/mathbot/file/1726054785738jaka9fl5.jpg

The graph shown in the image is a straight line passing through the origin and has a positive slope. To determine the type of symmetry, let's analyze the line's properties:

### Type of Symmetry:
The graph represents a line with the equation \( y = x \). This line has **rotational symmetry** about the origin (0, 0). This type of symmetry is also known as **odd symmetry**, meaning that if the graph is rotated 180 degrees around the origin, it looks the same.

In more technical terms, for a function to have odd symmetry, it must satisfy the condition \( f(-x) = -f(x) \). The line \( y = x \) meets this condition because \( -(-x) = x \).

**Summary:**
- The graph has **rotational symmetry** about the origin (odd symmetry).

Would you like more details or have any questions?

### Related Questions:
1. What is the difference between odd and even symmetry in graphs?
2. How can you determine the type of symmetry algebraically for any function?
3. What are some examples of functions that exhibit line symmetry?
4. Can a function have both line symmetry and point symmetry? If so, what is an example?
5. How do transformations affect the symmetry of a graph?

**Tip:** When determining symmetry, checking how the function behaves under transformations (like reflections or rotations) helps identify the type of symmetry it possesses.

Identify the type of symmetry for the graph of the function.

Learn how to identify the symmetry of a graph representing the linear equation y = x. This problem explores rotational symmetry about the origin and satisfies the condition for odd symmetry. Suitable for students in Grades 9-12.

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