Slope is one number answering one question: as you walk to the right along the line, how fast does it climb? Count the vertical change — the rise — count the horizontal change — the run — and divide. Drag either point below and watch the triangle, the fraction, and the line redraw together.
Two points make a slope
Why any two points give the same answer
Here is the reason the definition is allowed to exist. Pick a far-apart pair instead of a close pair and you build a bigger right triangle on the very same line — but it is the same shape, just scaled up. Both legs grow by the identical factor (here ×3), and multiplying top and bottom of a fraction by the same number never changes its value: 3 · 1 over 3 · 3 is still 1 over 3. So slope belongs to the line, not to the pair of points you happened to pick.
m = 0drag a point to begin
Point 1
x1−2
y1−1
Point 2
x24
y23
Drag the dots straight on the grid, or nudge the sliders with the arrow keys.
You can still drag the dots — the matching kind lights up on its own.