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.