Steepness as a Number

Some lines climb faster than others. The slope, written $m$, is the number that measures how fast a line climbs. Pick any two points on the line. The rise is how far you go up from the first point to the second. The run is how far you go right. The slope is the rise divided by the run.

$$m = \frac{rise}{run}$$

From (1, 1) to (3, 5): rise 4, run 2, slope 2

In the figure, go from (1, 1) to (3, 5). The rise is $5-1 = 4$ and the run is $3-1 = 2$, so $m = \frac{4}{2} = 2$. The line climbs 2 steps up for every 1 step right. You get the same slope from any two points on the line, because a straight line climbs at the same rate everywhere.