What Is a Linear Expression?
Before we dive into expressions with more than one variable, let's make sure we're solid on the basics.
A mathematical expression where each variable appears only to the first power (no exponents greater than 1, no square roots, no variables multiplied by each other). In a linear expression, all variables have a degree of exactly 1.
You've already worked with linear expressions like or . These have one variable — just or just .
Now we're going to level up and work with expressions that have more than one variable, like:
Think of each variable as representing a different unknown quantity. In science, we constantly deal with situations that involve multiple changing quantities at the same time — for example, the total distance travelled depends on both speed and time, or the total force on an object depends on multiple pushes and pulls. Multi-variable linear expressions help us describe exactly these kinds of relationships.
A linear expression is the building block of a linear equation. It is a linear equation (for example, ) that produces a straight-line graph — not the expression on its own. We'll explore that connection when we study equations.
Understanding Variables and Terms
Let's break down the building blocks of a multi-variable linear expression.
A letter (such as , , , ) that represents an unknown or changing value.
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.
The number multiplied by a variable. In the term , the coefficient is .
A term that is just a number with no variable attached. In , the constant is .
Let's label every part of the expression :
- → term with variable , coefficient is
- → term with variable , coefficient is
- → constant term
Always pay attention to the sign in front of a term. The sign belongs to the term! In , the second term is , not .
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