Slope

Property The slope $m$ of a line containing points $(x 1, y 1)$ and $(x 2, y 2)$ is given by the formula $m = \frac{y 2 y 1}{x 2 x 1}$.

Examples For points $(2, 4)$ and $(6, 6)$, the slope is $m = \frac{6 4}{6 2} = \frac{2}{4} = \frac{1}{2}$. For points $( 4, 4)$ and $(4, 2)$, the slope is $m = \frac{ 2 4}{4 ( 4)} = \frac{ 6}{8} = \frac{3}{4}$. For points $(0, 5)$ and $(5, 10)$, the slope is $m = \frac{10 ( 5)}{5 0} = \frac{15}{5} = 3$.

Explanation Think of slope as the ultimate measure of a line's steepness, or "rise over run." This formula calculates exactly that: for every step you take horizontally (the run), it tells you how many steps you go up or down (the rise). It’s a simple way to put a number to a slant.