Calculating the Gradient (Slope) The gradient ($m$) measures the rate of change between the vertical axis ($y$) and the horizontal axis ($x$). $m = \frac{y_2 - y_1}{x_2 - x_1}$ Interpretation: Positive ($m > 0$): Upward slope. Negative ($m Downward slope. Zero ($m = 0$): Horizontal line. Undefined: Vertical line. Understanding Gradient (Slope) To analyze the gradient (slope) of a line or curve, you are effectively measuring the rate of change between two variables: the vertical change (y) over the horizontal change (x). The Core Concept The gradient, commonly represented by the letter m , tells you how steep a line is and in which direction it is heading. In the context of a linear relationship, the formula is: Gradient (m) = (Change in y) / (Change in x) Or, using the coordinates of two points (x₁, y₁) and (x₂, y₂): m = (y₂ – y₁) / (x₂ – x₁) Interpr...