Which statement defines a single variable linear expression?

Which statement defines a single variable linear expression?

• A. The sum of a single variable term, where the variable has no exponent, and a constant (which may be zero).
• B. The sum of multiple variable terms with no exponents.
• C. The product of two variables.
• D. A variable in the denominator.

Answer: (A)

A linear expression in one variable has the variable appearing to the first power and only one such variable term, plus a constant. This matches the statement that describes a single variable term with no exponent, plus a constant. It’s basically the form ax + b, where a is the coefficient of the variable and b is the constant. The other ideas don’t fit because they involve either more than one variable, higher powers, or a division by the variable, which takes you out of the linear one-variable form. For example, a product of two variables is nonlinear, and a variable in the denominator creates a rational expression rather than a linear polynomial.

A linear expression in one variable has the variable appearing to the first power and only one such variable term, plus a constant. This matches the statement that describes a single variable term with no exponent, plus a constant. It’s basically the form ax + b, where a is the coefficient of the variable and b is the constant.

The other ideas don’t fit because they involve either more than one variable, higher powers, or a division by the variable, which takes you out of the linear one-variable form. For example, a product of two variables is nonlinear, and a variable in the denominator creates a rational expression rather than a linear polynomial.