1. The problem is to understand the formula for the slope of a line given two points $(x_1, y_1)$ and $(x_2, y_2)$. 2. The slope formula is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $m$ represents the slope. 3. This formula calculates the rate of change of $y$ with respect to $x$, or how much $y$ changes for a unit change in $x$. 4. Important rules: the denominator $x_2 - x_1$ cannot be zero because division by zero is undefined. This would mean the line is vertical and the slope is undefined. 5. To use the formula, subtract the $y$-coordinates of the two points to find the change in $y$, and subtract the $x$-coordinates to find the change in $x$. 6. Then divide the change in $y$ by the change in $x$ to get the slope. 7. For example, if the points are $(3, 4)$ and $(7, 10)$, then the slope is $$m = \frac{10 - 4}{7 - 3} = \frac{6}{4} = 1.5$$. 8. This means for every increase of 1 in $x$, $y$ increases by 1.5. 9. The slope tells us the steepness and direction of the line connecting the two points.