Slope is the change in y divided by the change in x between any two points on the line.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Keep the order
Subtract both coordinates in the same order, or the sign flips.
What the sign says
Positive rises left to right; negative falls. Steeper lines have a larger size, whatever the sign.
Flat and vertical
A horizontal line has slope 0. A vertical line has no slope at all, because the run is zero.
The formula and what it computes
Slope is (y₂ − y₁)/(x₂ − x₁): the vertical change divided by the horizontal change. It measures how steeply the line rises per unit moved right, and it is the same wherever on the line you measure it.
Keep the point order consistent
Use the same point first in both subtractions. Mixing the order negates only one part and gives the wrong sign. Swapping both is fine — the two negations cancel — which is why either point may go first.
Interpreting the number
A slope of 3 means up 3 for every 1 across. A slope of −1/2 means down 1 for every 2 across. Reading it as a rate rather than an abstract number is what makes slope useful in modelling.
Zero and undefined
A horizontal line has slope 0; a vertical line has undefined slope, since the denominator is zero. These are genuinely different situations, and calling a vertical line "slope infinity" is wrong rather than merely informal.
Step 2: Try It Yourself
Tap and try it out.
Both triangles give the same slope, 2, even though one is bigger. They are the same shape, so their sides are in the same ratio.
Step 3: Watch an Example
One step at a time.
Watch Dev Find a Negative Slope
A line passes through (1, 9) and (4, 0).
- Step 1
He takes the change in y first: 0 − 9 = −9.
Step 4: Your Turn
Practice makes it stick.
Rising
Problem 1 of 2
Through (0, 0) and (2, 8). Slope?
Flat
Problem 2 of 2
Through (1, 6) and (9, 6). Slope?
Rise over Run
1 of 8
Through (0, 1) and (3, 10). Slope?
2 of 8
Through (2, 8) and (6, 0). Slope?
3 of 8
Through (5, 2) and (5, 9). Does the slope exist? 1 for yes, 0 for no.
4 of 8
Through (0, 4) and (8, 4). Slope?
5 of 8
Through (1, 1) and (4, 13). Slope?
6 of 8
Sort each line by its slope.
Tap something to move it.
- Empty
- Empty
- Empty
7 of 8
Of slopes 2 and 6, which line is steeper? Give the number.
8 of 8
Through (3, 7) and (5, 3). Slope?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Through (0, 2) and (4, 14). Slope?
What You Learned
- Slope is the change in y over the change in x.
- Subtract both coordinates in the same order or the sign flips.
- Horizontal lines have slope zero; vertical lines have none.