The slope of a line is found by calculating the ratio of the vertical change to the horizontal change between two points on the line. This is also known as the rise over run. To find the slope mmm between 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:

• y2−y1y_2-y_1y2​−y1​ is the change in the y-coordinates (rise)
• x2−x1x_2-x_1x2​−x1​ is the change in the x-coordinates (run)

Essentially, you subtract the y-values of the two points and divide by the difference of the x-values. This gives you the steepness or slope of the line. For example, if the points are (2, 5) and (9, 19):

m=19−59−2=147=2m=\frac{19-5}{9-2}=\frac{14}{7}=2m=9−219−5​=714​=2

So the slope is 2. If you have a line equation, you can also rewrite it in slope-intercept form y=mx+by=mx+by=mx+b, where mmm is the slope. This method is the standard way to find slope in algebra and coordinate geometry.