how to find slope with two points

To find the slope of a line given two points (x1,y1)(x_1,y_1)(x1​,y1​) and (x2,y2)(x_2,y_2)(x2​,y2​), use the formula:

m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}m=x2​−x1​y2​−y1​​

Here:

• mmm is the slope of the line.
• y2−y1y_2-y_1y2​−y1​ is the difference in the y-coordinates (rise).
• x2−x1x_2-x_1x2​−x1​ is the difference in the x-coordinates (run).

Steps:

1. Label the coordinates of the first point as (x1,y1)(x_1,y_1)(x1​,y1​) and the second as (x2,y2)(x_2,y_2)(x2​,y2​).
2. Calculate the difference y2−y1y_2-y_1y2​−y1​.
3. Calculate the difference x2−x1x_2-x_1x2​−x1​.
4. Divide the difference in y-coordinates by the difference in x-coordinates to find the slope mmm.

Note: The order in which points are chosen does not affect the slope as long as the subtraction is done consistently. Example:
For points (1,−2)(1,-2)(1,−2) and (3,−6)(3,-6)(3,−6),

m=−6−(−2)3−1=−6+22=−42=−2m=\frac{-6-(-2)}{3-1}=\frac{-6+2}{2}=\frac{-4}{2}=-2m=3−1−6−(−2)​=2−6+2​=2−4​=−2

So the slope is −2-2−2.