Which statement best describes the purpose of the gradient formula?

The gradient formula is primarily used to calculate the rate of change between two points on a graph. In mathematical terms, the gradient, or slope, of a line is determined by the change in the y-values divided by the change in the x-values between two points. This concept is fundamental in calculus and can be applied to understand how one quantity changes in relation to another.

For example, if you have two points on a line defined by their coordinates (x₁, y₁) and (x₂, y₂), the gradient is calculated using the formula (y₂ - y₁) / (x₂ - x₁). This value gives insight into how steep the line is and indicates whether the value of y increases or decreases as x changes.

The other options do not accurately reflect the function of the gradient formula. Finding the area of a triangle requires different geometric principles, determining the volume of a shape involves measuring three-dimensional space, and performing break-even analysis is a financial concept related to costs and revenues, none of which directly relate to the calculation of gradients or slopes.