Which of the following equations does not represent a straight line?

The equation that does not represent a straight line is indeed the one given in the answer. This is due to its mathematical form, which includes a variable raised to a power greater than one. Specifically, the equation (y = x^2 + 3) is a quadratic equation, defining a parabola rather than a straight line.

In contrast, the other equations represent linear relationships. They can be rearranged into the standard form of a line, which is (y = mx + b), where (m) is the slope and (b) is the y-intercept. The equation (3x + 2y = 8) can be rearranged to show (y = -\frac{3}{2}x + 4), indicating a straight line with a specific slope and intercept. The equation (y = x/2 - 5) is already in slope-intercept form, clearly representing a straight line. Lastly, (x = 4y) can be rearranged to (y = \frac{1}{4}x), again demonstrating a linear relationship.

Thus, the distinction is that linear equations produce straight lines on a graph, while quadratic equations represent curves,