Linear expressions with more than one variable

Before we dive into expressions with more than one variable, let's make sure we're solid on the basics.

Linear Expression: A mathematical expression where each variable is raised to the power of 1 (no exponents, no square roots, no variables multiplied by each other). The expression forms a straight line when graphed.

You've already worked with linear expressions like $3x+5$ or $2y-7$. These have one variable , just $x$ or just $y$.

Now we're going to level up and work with expressions that have more than one variable, like:

• $3x+2y$
• $4a-b+7$
• $2m+5n-3p$

Think of each variable as representing a different unknown quantity. In real life, we often deal with situations that involve multiple changing quantities at the same time , and that's exactly what these expressions help us describe.

Let's break down the building blocks of a multi-variable linear expression.

Variable: A letter (such as $x$, $y$, $a$, $b$) that represents an unknown or changing value.

Term: A single part of an expression, separated by $+$ or $-$ signs. A term can be a number, a variable, or a number multiplied by a variable.

Coefficient: The number multiplied by a variable. In the term $5x$, the coefficient is $5$.

Constant: A term that is just a number with no variable attached. In $3x+2y+9$, the constant is $9$.

Let's label every part of the expression $4a-3b+10$:

• $4a$ → term with variable $a$, coefficient is $4$
• $-3b$ → term with variable $b$, coefficient is $-3$
• $10$ → constant term