Linear representations refer to the way data or mathematical objects can be expressed in a straight-line format, often using equations or graphs. In mathematics, this concept is commonly applied in algebra and geometry, where relationships between variables can be depicted as linear functions. These functions typically take the form of y = mx + b, where m represents the slope and b the y-intercept. In computer science, linear representations are crucial for organizing data efficiently. For example, arrays and linked lists are linear data structures that store elements in a sequential manner. This organization allows for straightforward access and manipulation of data, making it easier to perform operations like searching and sorting.