What is slope?
How steep is it? Count how far the line climbs for every step it takes across. Move either dot and the two numbers behind the steepness show themselves.
Slope 4 4 = 1no number exists for it
Up 1 for every 1 across.
- Rise (up/down)
- 1
- Run (across)
- 1
- Crosses y-axis at
- 0
- Equation
- y = x
Jump to a line
Ready to try some? Slope & y-intercept worksheets
Where it usually goes wrong
Steepness gets read off the picture instead of counted. Two lines drawn on differently scaled axes can look equally steep and have nothing in common, and a line going down is often called “steeper” than one going up at the same angle. Slope is a count — how far up for one step across — and its sign is a direction, not a size.
Try this
- Press Flat. The rise is 0 and the run is not, so the slope is 0 — which is a number, and different from having no slope at all.
- Now press Vertical. The run is 0, and the tool stops giving a number: there is no answer to “how far up for one step across” when you cannot take the step.
- Drag point B to the other side of point A. Rise and run both change sign, the fraction does not, and it is the same line it always was.
Where this goes next
Every rate is this: cents per gram, miles per hour, the slope of a line on a graph in science. Slope is the first one that gets a picture, and the picture is the one that has to stick.