Determine if the following equation is linear.

4x+y3+7y=9/4𝑥+𝑦3+7𝑦=9

The given equation seems to be:

\[ 4x + y^3 + 7y = 9 \]

To determine if an equation is linear, all the variables in the equation must be of the first degree, meaning the powers of the variables (such as \( x \) and \( y \)) should be 1.

### Analysis of each term:
- **\( 4x \)**: The power of \( x \) is 1, so this term is linear.
- **\( y^3 \)**: The power of \( y \) is 3, so this term is **not linear**. A power greater than 1 makes the equation nonlinear.
- **\( 7y \)**: The power of \( y \) is 1, so this term is linear.
- **\( 9 \)**: This is a constant and doesn't affect the linearity.

### Conclusion:
Because the term \( y^3 \) has a power greater than 1, the equation is **not linear**.

Would you like further explanation on why nonlinear terms affect the equation?

Here are 5 related questions for further practice:
1. How do you classify equations based on their degree?
2. What makes an equation quadratic or cubic?
3. What would make a system of equations linear?
4. Can a linear equation have a variable in the denominator?
5. What are the main features of a linear function's graph?

**Tip:** Always check the powers of all variables when determining if an equation is linear.

Determine if the following equation is linear: 4x + y^3 + 7y = 9

Explore whether the equation 4x + y^3 + 7y = 9 is linear by analyzing the powers of the variables. This algebra problem covers the difference between linear and nonlinear equations, focusing on identifying terms that affect linearity. Suitable for Grades 8-10.

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