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Let's analyze each equation to determine if it is linear or not.

### Definition:
A **linear equation** is one where each term is either a constant or the product of a constant and a single variable. No variables should be raised to powers greater than 1, multiplied together, or appear in the denominator.

Now let's evaluate the given equations:

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### (a) \( 9x + 7 + 8y = x - 5 \)
- Rearrange: \( 9x - x + 8y + 7 = -5 \), simplifying to \( 8x + 8y + 7 = -5 \), which is a linear equation.
- **Answer**: Linear (Yes)

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### (b) \( y = 9xy + 6 \)
- There is a product term \( 9xy \), which makes it nonlinear because variables \( x \) and \( y \) are multiplied together.
- **Answer**: Nonlinear (No)

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### (c) \( x + \frac{7}{y} = 0 \)
- The variable \( y \) is in the denominator, making this equation nonlinear.
- **Answer**: Nonlinear (No)

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### (d) \( y^2 + 2x = 9 \)
- The term \( y^2 \) (a variable raised to the power of 2) makes this equation nonlinear.
- **Answer**: Nonlinear (No)

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### Summary of answers:
- (a) Yes
- (b) No
- (c) No
- (d) No

Would you like further explanation on any of the points? 

Here are 5 related questions you could explore:
1. How can you graph a linear equation?
2. What makes an equation nonlinear?
3. Can two variables in a product ever form a linear equation?
4. How does rearranging an equation help determine its linearity?
5. What are examples of systems of linear equations?

**Tip**: For an equation to be linear, no variables should be squared, cubed, or appear in denominators or multiplied together.

For each equation, determine whether it is linear. The equations are: (a) 9x + 7 + 8y = x - 5 (b) y = 9xy + 6 (c) x + 7/y = 0 (d) y^2 + 2x = 9

Learn how to determine whether an equation is linear or nonlinear. Explore examples such as 9x + 7 + 8y = x - 5 and y^2 + 2x = 9, and understand the differences between linear and nonlinear equations. Suitable for students in Grades 8-10.

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