Slope from Two Points: Rise Over Run
Given (x1,y1) and (x2,y2), slope m = (y2-y1)/(x2-x1).
Equation
y = x
Graph
Table
| x | y |
|---|---|
| -5 | -5 |
| -4 | -4 |
| -3 | -3 |
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
What this lesson covers
What you do
You shape the function y = m*x + c and watch the graph answer.
Challenges to clear
- Rise over run: make the line have slope 3 AND pass through (1, 2) — the intercept becomes −1.
- Climb one step right: the same line hits (2, 5) — rise 3 for run 1.
- Rise over run: from (2, 3) to (3, 7) the line climbs 4 for every 1 across. Set the slope to 4.
- Now slide the intercept until the line actually passes (2, 3). Slope alone does not fix a line — it needs a point too.
Check yourself
What does slope = (y2 - y1)/(x2 - x1) measure geometrically?
- Rise over run — vertical change divided by horizontal change as you move from one point to the other. — correct
- The distance between the two points.
- The midpoint of the two points.
- The angle of the line in degrees.
Think about it
- For points (1, 2) and (4, 11): slope = (11−2)/(4−1) = 9/3 = 3.