The expression you provided, \(3x - 4y\), is a linear expression involving two variables, \(x\) and \(y\). Here's what this expression means and some additional insights:

### Understanding the Expression

1. **Coefficients and Variables:**
   - The expression \(3x - 4y\) consists of two terms: \(3x\) and \(-4y\).
   - In \(3x\), the coefficient is \(3\) and the variable is \(x\).
   - In \(-4y\), the coefficient is \(-4\) and the variable is \(y\).

2. **Linear Nature:**
   - This expression is linear because it involves variables raised only to the first power. There are no squares, cubes, or higher powers of \(x\) or \(y\).

3. **Algebraic Operations:**
   - The expression can represent a variety of mathematical operations, such as evaluating for specific values of \(x\) and \(y\), or being part of an equation where you solve for one variable in terms of the other.

### Potential Uses of the Expression

- **Substitution:** If values for \(x\) and \(y\) are provided, you can substitute these values into the expression to calculate a specific result.
- **Equation Setup:** The expression could be part of an equation, such as \(3x - 4y = 0\), which could be solved for one of the variables.
- **Graphing:** When used in an equation like \(3x - 4y = 0\), it represents a straight line in the \(xy\)-plane.

Would you like to explore any specific operations or questions related to this expression?

### Related Questions to Consider

1. How do you solve the equation \(3x - 4y = 0\) for \(x\) in terms of \(y\)?
2. What is the slope of the line represented by the equation \(3x - 4y = 0\)?
3. If \(x = 2\) and \(y = -1\), what is the value of the expression \(3x - 4y\)?
4. How can the expression \(3x - 4y\) be used in solving a system of linear equations?
5. What does the expression \(3x - 4y\) represent geometrically in three-dimensional space if \(z = 3x - 4y\)?

### Tip

When dealing with algebraic expressions, it’s helpful to know what operations you want to perform with them—whether it’s solving for a variable, graphing the expression, or substituting values. This will guide you in using the expression correctly and effectively.

Explore the algebraic expression 3x - 4y and its operations. This linear equation involves variables x and y with coefficients 3 and -4 respectively. Learn how to substitute values, set up equations, and understand its graphing implications. Ideal for Grades 7-9.

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