Which of the following equations represents a linear function?

The equation that represents a linear function is one that can be expressed in the form ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. In this case, the equation ( y = 3x + 2 ) fits this definition perfectly. Here, the coefficient of ( x ) (which is 3) represents the slope of the line, indicating how steep the line will be, and the constant term (which is 2) represents the point where the line crosses the y-axis.

Linear functions graph as straight lines, and they display a constant rate of change. In the equation ( y = 3x + 2 ), for every unit increase in ( x ), ( y ) increases by 3 units, demonstrating this constant rate of change.

In contrast, the other equations represent different kinds of functions. The equation ( y = x² ) represents a quadratic function with a parabolic graph, which is not linear. The equation ( y = |x| ) signifies an absolute value function, which also does not form a straight line. Lastly, ( y = x³ ) illustrates a cubic function, which creates a