Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which equation represents a linear function?

1. y = x² + 3

2. y = 2x + 5

3. y = 1/x

4. y = 3sin(x)

The correct answer is: y = 2x + 5

A linear function is defined by an equation that can be graphically represented as a straight line. This means that it must be in the form of y = mx + b, where m represents the slope and b represents the y-intercept. The equation y = 2x + 5 fits this definition perfectly. Here, 2 is the slope, indicating how steep the line is, and 5 is the y-intercept, telling us where the line crosses the y-axis. This relationship maintains a constant rate of change between y and x, which is characteristic of linear functions. In contrast, y = x² + 3 is a quadratic function, which produces a parabolic graph rather than a straight line. Similarly, y = 1/x represents a hyperbola, resulting in a graph that approaches the axes asymptotically and does not form a straight line. Lastly, y = 3sin(x) is a trigonometric function that oscillates, creating a wave-like pattern instead of a linear relationship. Thus, the only equation that represents a linear function is y = 2x + 5.