Which of the following equations represents a linear function?

A linear function is defined as a function that can be graphically represented as a straight line on a coordinate plane. The general form of a linear function is y = mx + b, where m represents the slope and b represents the y-intercept.

The equation y = 2x + 1 is in this format, where 2 is the slope and 1 is the y-intercept. This indicates that for every increase of 1 in the x-coordinate, the value of y increases by 2. The graph of this function will be a straight line, which is characteristic of linear functions.

In contrast, the other equations represent different types of functions. For example, y = x^2 + 3 is a quadratic function because it includes the squared term, which produces a parabolic graph rather than a straight line. The equation y = |x - 4| defines an absolute value function, which results in a V-shaped graph, again indicating non-linearity. Lastly, y = 3sin(x) is a sinusoidal function, producing a wave-like pattern instead of a line.

Thus, the equation that accurately represents a linear function among the given options is indeed y = 2x + 1.