Which of the following expressions describes a linear function?

A linear function is defined by an equation of the form y = mx + b, where m and b are constants and m represents the slope of the line, while b represents the y-intercept. In this context, the expression that accurately fits this definition is y = 5x.

This equation clearly outlines a straight line with a slope of 5 and a y-intercept of 0, indicating that for every unit increase in x, y increases by 5. The absence of any squared, cubic, fractional, or root terms confirms that this function is linear.

The other given expressions do not meet the criteria for linearity due to their respective forms. For instance, the first expression contains x², indicating a quadratic function, while the third expression involves division by x, suggesting a hyperbolic function. Lastly, the fourth expression incorporates a square root, which results in a curve rather than a straight line. Thus, of all the options, only y = 5x represents a linear function.