To find the slope with two points, you use a simple formula and plug in the coordinates.

Step 1: Know the slope formula

If your two points are
(x1,y1)(x_1,y_1)(x1​,y1​) and (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​​

This is often described as “rise over run”: change in y divided by change in x.

Step 2: Label your points

Take your actual points and label them consistently. Example: Suppose your two points are (1,−2)(1,-2)(1,−2) and (3,−6)(3,-6)(3,−6).

  • Let (x1,y1)=(1,−2)(x_1,y_1)=(1,-2)(x1​,y1​)=(1,−2)
  • Let (x2,y2)=(3,−6)(x_2,y_2)=(3,-6)(x2​,y2​)=(3,−6)

You could swap them (make the first one point 2 and the second one point 1) and you’d still get the same slope as long as you stay consistent in the formula.

Step 3: Plug into the formula

Using the example (1,−2)(1,-2)(1,−2) and (3,−6)(3,-6)(3,−6):

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 is −2-2−2.

Step 4: Important tips and special cases

  • It doesn’t matter which point is “point 1” and which is “point 2” as long as you use them in the same order in numerator and denominator.
  • If x2−x1=0x_2-x_1=0x2​−x1​=0, then you are dividing by zero, which means the line is vertical and the slope is undefined.
  • You may also see the equivalent form y1−y2x1−x2\frac{y_1-y_2}{x_1-x_2}x1​−x2​y1​−y2​​; it gives the same answer because you’re multiplying top and bottom by −1-1−1.

Quick mini story to remember it

Imagine walking up or down a hill between two spots on a hiking trail.

  • The change in height (up or down) is your rise (y2−y1y_2-y_1y2​−y1​).
  • The distance forward along the trail is your run (x2−x1x_2-x_1x2​−x1​).

Slope is just “how steep that hill feels” = rise ÷ run.

Very short version (TL;DR)

  • Label your points (x1,y1)(x_1,y_1)(x1​,y1​), (x2,y2)(x_2,y_2)(x2​,y2​).
  • Compute m=y2−y1x2−x1m=\dfrac{y_2-y_1}{x_2-x_1}m=x2​−x1​y2​−y1​​.
  • Simplify the fraction; if the denominator is 0, the slope is undefined.

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