Which of the following equations represents a linear relationship?

A linear relationship is represented by an equation of the first degree in which the highest power of the variable is one. In this context, the equation that best fits this definition is the one given.

The equation 2x + 5 = 9 is a straightforward linear equation. When rearranged, it can be expressed in the standard linear form y = mx + b, where m is the slope and b is the y-intercept. In this case, if you subtract 5 from both sides, you get 2x = 4, and dividing both sides by 2 gives you x = 2. This indicates a linear relationship where the graph is a straight line.

The other equations presented do not form linear relationships. The equation x² + 3x + 2 = 0 involves a squared term, indicating it is quadratic and represents a parabola when graphed. Similarly, 3x² - 4 = 0 is another quadratic equation, and y = 4x² + 2x + 1 is a polynomial of degree two, also resulting in a parabola. None of these equations can be represented as a straight line since they involve squared terms, making them non-linear.