Which of the following represents a linear expression?

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Multiple Choice

Which of the following represents a linear expression?

A linear expression is defined as an algebraic expression in which each term is either a constant or the product of a constant and a single variable raised to the first power. In the case of the identified correct answer, the expression \(y = 3x + 3\) is linear because it follows the standard form of a linear equation: it consists of the variable \(x\) raised to the first power, and the terms are combined through addition. It can also be represented graphically as a straight line. Options that involve variables raised to powers greater than one, such as quadratic functions (like \(y = x^2\) or \(y = x^2 + 4\)), or involve division by a variable (like \(y = 2/x\)), do not meet the criteria for linearity. Quadratic expressions graph as parabolas, while the expression involving division results in a hyperbola. Thus, the presence of degrees higher than one or the manipulation of variables in a non-linear manner sets those options apart from the linear expression presented in the correct choice.

A linear expression is defined as an algebraic expression in which each term is either a constant or the product of a constant and a single variable raised to the first power. In the case of the identified correct answer, the expression (y = 3x + 3) is linear because it follows the standard form of a linear equation: it consists of the variable (x) raised to the first power, and the terms are combined through addition. It can also be represented graphically as a straight line.

Options that involve variables raised to powers greater than one, such as quadratic functions (like (y = x^2) or (y = x^2 + 4)), or involve division by a variable (like (y = 2/x)), do not meet the criteria for linearity. Quadratic expressions graph as parabolas, while the expression involving division results in a hyperbola. Thus, the presence of degrees higher than one or the manipulation of variables in a non-linear manner sets those options apart from the linear expression presented in the correct choice.

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