Final answer:
A horizontal asymptote is a horizontal line that a function approaches as the independent variable moves towards infinity or negative infinity, but never actually reaches.
Step-by-step explanation:
A horizontal asymptote is a horizontal line that a function approaches but never actually reaches as the independent variable (usually x) heads towards infinity or negative infinity. In formal terms, if the y-value approaches a constant value as the value of x increases or decreases without bound, the line y = that constant value is considered to be a horizontal asymptote of the function.
For example, with the function y = 1/x, as x approaches infinity, the value of y approaches 0, but never actually reaches 0. Here, the line y = 0 is a horizontal asymptote of the function. The horizontal asymptote is not dependent on the slope (m) or y-intercept (b) of a line, which are terms used to describe the characteristics of straight-line equations such as y = mx + b.