Determine whether the graph of
each equation is symmetric with
respect to the origin: 5x-3y=5

To determine if the graph of the equation \( 5x - 3y = 5 \) is symmetric with respect to the origin, we follow a specific test:

### Steps:

1. **Substitute** \((-x, -y)\) for \((x, y)\) into the equation.
   
   The original equation is:
   \[
   5x - 3y = 5
   \]
   
   Substituting \((-x, -y)\) for \((x, y)\):
   \[
   5(-x) - 3(-y) = 5
   \]
   Simplifying:
   \[
   -5x + 3y = 5
   \]
   
2. **Compare** this result with the original equation. The new equation is \( -5x + 3y = 5 \), which is **not the same** as the original equation \( 5x - 3y = 5 \).

### Conclusion:
Since the equation is not unchanged by this substitution, the graph of the equation \( 5x - 3y = 5 \) is **not symmetric with respect to the origin**.

Would you like any further clarification or details?

Here are 5 related questions to further your understanding:
1. How do you test symmetry with respect to the x-axis for equations?
2. How do you test symmetry with respect to the y-axis for equations?
3. What are the general types of symmetries possible in a graph?
4. Can you determine symmetry visually from a graph without algebra?
5. What is the graphical meaning of symmetry with respect to the origin?

**Tip**: Symmetry with respect to the origin occurs when replacing both \(x\) with \(-x\) and \(y\) with \(-y\) yields the same equation.

Determine whether the graph of each equation is symmetric with respect to the origin: 5x - 3y = 5

Explore how to determine whether the graph of the equation 5x - 3y = 5 is symmetric with respect to the origin. This problem involves algebraic concepts like symmetry in graphs and linear equations. Step-by-step solutions make this suitable for Grades 9-12.

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