1. The problem is to calculate the slope of a line given two points or from a graph. 2. The formula for slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Important rules: - The slope measures how steep the line is. - It is the ratio of the vertical change (rise) to the horizontal change (run). - If $x_2 = x_1$, the slope is undefined because division by zero is not allowed. 4. Example: Suppose you have points $(2, 3)$ and $(5, 11)$. Calculate the difference in $y$ values: $$y_2 - y_1 = 11 - 3 = 8$$ Calculate the difference in $x$ values: $$x_2 - x_1 = 5 - 2 = 3$$ 5. Substitute into the slope formula: $$m = \frac{8}{3}$$ 6. This means the slope of the line passing through these points is $\frac{8}{3}$, which means for every 3 units you move horizontally, the line rises 8 units vertically. This is how you calculate the slope of a line.