Which of the following expressions represents a linear equation?

Which of the following expressions represents a linear equation?

• A. y = 2x² + 3
• B. y = 3x - 5
• C. y = 1/x
• D. y = √x + 2

Answer: (B)

A linear equation is characterized by its highest degree being one, which means that the variable(s) in the equation are to the first power. In the expression that represents a linear equation, any term involving the variable appears as a single linear term, and there are no products of variables, no variables in denominators, or no square roots of variables. The expression that correctly exemplifies a linear equation, y = 3x - 5, fits this definition perfectly. It consists of a variable x raised to the first power, along with a constant term (-5). The absence of any squared terms, radical expressions, or fractional terms makes it a straightforward representation of a line when graphed. In contrast, the other expressions fail to meet this criterion: - The first expression includes x squared, making it a quadratic equation. - The third expression features a variable in the denominator, which makes it a rational equation, not linear. - The fourth expression contains a square root of x, indicating it is not linear since it introduces a variable under a root. Thus, the expression y = 3x - 5 is the only choice that represents a linear equation.

A linear equation is characterized by its highest degree being one, which means that the variable(s) in the equation are to the first power. In the expression that represents a linear equation, any term involving the variable appears as a single linear term, and there are no products of variables, no variables in denominators, or no square roots of variables.

The expression that correctly exemplifies a linear equation, y = 3x - 5, fits this definition perfectly. It consists of a variable x raised to the first power, along with a constant term (-5). The absence of any squared terms, radical expressions, or fractional terms makes it a straightforward representation of a line when graphed.

In contrast, the other expressions fail to meet this criterion:

• The first expression includes x squared, making it a quadratic equation.

• The third expression features a variable in the denominator, which makes it a rational equation, not linear.

• The fourth expression contains a square root of x, indicating it is not linear since it introduces a variable under a root.

Thus, the expression y = 3x - 5 is the only choice that represents a linear equation.