The steepness of a line on a graph, representing the rate of change of one variable with respect to another, is quantified by its gradient. A horizontal line has a gradient of zero, while a vertical line’s gradient is undefined. For example, a line rising two units vertically for every one unit of horizontal movement has a gradient of two.
Understanding this concept is fundamental to numerous fields, including calculus, physics, and engineering. It allows for the modeling and prediction of various phenomena, from the trajectory of a projectile to the rate of a chemical reaction. Historically, the development of this mathematical concept was crucial for advancements in fields like navigation and construction, where accurate calculations of angles and inclines were essential.
