Final answer:
A horizontal asymptote on a graph is a horizontal line that the graph approaches but does not touch as x approaches infinity. It indicates the limiting value of the function. This concept is distinct from the equation of a straight line which extends indefinitely without an asymptote.
Step-by-step explanation:
A horizontal asymptote on a graph represents a line that the graph approaches but does not touch as the values of x move towards positive or negative infinity. It illustrates the behavior of a function as the input grows very large in the positive or negative direction. This can occur in various kinds of functions, such as rational functions where the degree of the numerator is less than or equal to the degree of the denominator. The horizontal asymptote can be a horizontal line at some positive value (d), a horizontal line at some negative value (c), or at the x-axis itself if the value approached is zero.
The equation for a straight line, y = mx + b, where m represents the slope and b represents the y-intercept, does not feature horizontal asymptotes because the line continues indefinitely without approaching a specific horizontal value. However, in the context of functions such as y = (ax^2+bx+c)/(dx+e), where the degree of the polynomial in the numerator is less than or equal to that in the denominator, the line y = a/d could be a horizontal asymptote as x approaches infinity.