To find the slope between two points, you use a simple formula that measures how steep the line is that connects them.

Core idea

If you have two points on a line:

  • First point: (x1,y1)(x_1,y_1)(x1​,y1​)
  • Second point: (x2,y2)(x_2,y_2)(x2​,y2​)

Then the slope mmm is:

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

People often call this “rise over run,” where:

  • Rise = change in y = y2−y1y_2-y_1y2​−y1​
  • Run = change in x = x2−x1x_2-x_1x2​−x1​

Step‑by‑step example

Say your two points are (1,−2)(1,-2)(1,−2) and (3,−6)(3,-6)(3,−6).

  1. Label the points:
    • (x1,y1)=(1,−2)(x_1,y_1)=(1,-2)(x1​,y1​)=(1,−2)
    • (x2,y2)=(3,−6)(x_2,y_2)=(3,-6)(x2​,y2​)=(3,−6)
  2. Plug into the formula:

m=y2−y1x2−x1=−6−(−2)3−1=−6+22=−42=−2m=\frac{y_2-y_1}{x_2-x_1} =\frac{-6-(-2)}{3-1} =\frac{-6+2}{2} =\frac{-4}{2} =-2m=x2​−x1​y2​−y1​​=3−1−6−(−2)​=2−6+2​=2−4​=−2

So the slope of the line through those two points is −2-2−2.

Important details and special cases

  • It does not matter which point you call “point 1” and which “point 2,” as long as you stay consistent in the formula (the x and y from the same point must go together).
  • If x2−x1=0x_2-x_1=0x2​−x1​=0, that means the line is vertical and the slope is undefined (you cannot divide by zero).
  • If y2−y1=0y_2-y_1=0y2​−y1​=0, that means the line is horizontal and the slope is 000.

Quick mini‑story to remember it

Imagine you’re hiking a straight trail on a hill from one marker to another:

  • The change in height between markers is your “rise” (y2−y1y_2-y_1y2​−y1​).
  • The distance forward you walk is your “run” (x2−x1x_2-x_1x2​−x1​).
  • The steepness of the trail is the slope: rise ÷ run.

A positive slope means you’re going uphill as you move to the right; a negative slope means downhill.

Tiny checklist

When you’re given two points and asked “how to find the slope of two points,” do this:

  1. Write the two points and label them (x1,y1)(x_1,y_1)(x1​,y1​) and (x2,y2)(x_2,y_2)(x2​,y2​).
  1. Compute y2−y1y_2-y_1y2​−y1​.
  2. Compute x2−x1x_2-x_1x2​−x1​.
  3. Divide: slope m=y2−y1x2−x1m=\dfrac{y_2-y_1}{x_2-x_1}m=x2​−x1​y2​−y1​​.
  4. Simplify the fraction and check if the line is vertical (undefined) or horizontal (0).

TL;DR:
Use m=y2−y1x2−x1m=\dfrac{y_2-y_1}{x_2-x_1}m=x2​−x1​y2​−y1​​, plug in your two points, and simplify; that’s exactly how to find the slope of two points in any basic algebra or graphing problem.

Information gathered from public forums or data available on the internet and portrayed here.