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The question asks which one of Marie's equations is linear. To determine whether an equation is linear, we check if the equation represents a straight line when graphed. A linear equation should have variables to the power of 1 and no products between variables.

Let's go through the options:

1. \( \frac{4}{x} + \frac{y}{7} = \frac{-1}{11} \)  
   - This equation contains a term with \( \frac{4}{x} \), which makes it non-linear because a variable \( x \) in the denominator is a characteristic of a rational function, not a linear one.

2. \( 4x + 7y = \frac{-1}{11} \)  
   - This equation is linear because both variables \( x \) and \( y \) have a power of 1, and there are no products between variables.

3. \( 4x^2 + 7y = -11 \)  
   - This equation is non-linear because the term \( x^2 \) involves a squared variable, which makes it quadratic.

4. \( 4^x + \frac{y}{7} = -11 \)  
   - This equation is non-linear because the term \( 4^x \) involves an exponential function, which is not linear.

The correct answer is:  
**Option 2: \( 4x + 7y = \frac{-1}{11} \)**

Do you need further details or have any other questions? Here are some follow-up questions you might find useful:

1. What is the general form of a linear equation?
2. How can we identify non-linear terms in an equation?
3. Why is having a variable in the denominator problematic for linearity?
4. What are some common forms of non-linear equations?
5. How does the graph of a linear equation differ from that of a quadratic or exponential equation?

**Tip:** Always check for exponents, products, and variable denominators when determining whether an equation is linear!

Marie's equations are listed below. Which one is linear?

1. 4/x + y/7 = -1/11
2. 4x + 7y = -1/11
3. 4x^2 + 7y = -11
4. 4^x + y/7 = -11

This problem focuses on identifying which of the four equations provided by Marie is linear. The problem involves recognizing linearity in algebraic expressions, and distinguishing between linear and non-linear terms, such as variables in denominators and exponents. Suitable for Grades 8-10.

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