What does it mean on a graph to have infinite solutions? Explain what you would see.
Having infinite solutions on a graph means that the lines or equations being represented intersect each other at every point along the graph. This implies that regardless of the value on the x-axis, there will always be a corresponding y-value that satisfies all equations involved.
Visually, on a graph infinite solutions can be represented as overlapping lines or equations that coincide perfectly on top of each other. This creates a single line on the graph where all points along it are solutions to all equations involved. In other words, the lines or equations do not have a distinct point of intersection but rather intersect at every possible point on the graph.
This phenomena typically occurs when the equations being graphed are essentially the same or are multiples of each other, leading to an infinite number of solutions that satisfy them all simultaneously.