1. The problem asks: Why do we divide when calculating the gradient (slope) of a line? 2. The gradient formula is given by: $$\text{gradient} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. This formula measures how much the vertical value ($y$) changes for a given horizontal change ($x$). 4. We divide because the gradient is a ratio of vertical change to horizontal change, showing the steepness of the line. 5. Dividing the difference in $y$ by the difference in $x$ normalizes the vertical change per unit horizontal change. 6. This means the gradient tells us how many units $y$ changes when $x$ changes by one unit. 7. Without division, we would only have the raw difference in $y$, which doesn't account for how far apart the $x$ values are. 8. Therefore, division is essential to express the slope as a rate of change, making it a meaningful and comparable measure.