Ontario Mathematics Proficiency Practice Test

The equation y = 2x + 3 represents a linear relationship because it follows the standard form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2, which indicates that for every unit increase in x, y increases by 2 units. The y-intercept is 3, meaning the line crosses the y-axis at the point (0, 3).

Linear relationships are characterized by a constant rate of change, which means that the graph of the equation forms a straight line. In contrast, the other equations do not describe linear relationships because they involve non-linear expressions. The equation y = x² + 2 is a quadratic equation, forming a parabola when graphed. The equation y = sqrt(x) represents a square root function, which has a curved shape and is defined only for non-negative values of x. Lastly, the equation y = 1/x describes a hyperbolic relationship, which has two distinct branches and is not linear. Thus, only y = 2x + 3 clearly represents a linear relationship.