Slope Is a Rate

Lesson 2 of 10 · 7 min · Free, no account needed

What you will learn

Slope is how much a line climbs for one step to the right.
Slope is a rate of change: dollars per km, error per training round.
Over several steps, slope = rise ÷ run. A falling line has a negative slope.

Two taxi apps, one 9 km ride. Which one do you take?
Tap the app you bet is cheaper.
Now ride it. Drag the taxis to the flag.
Watch the meters and the graph under the road grow together.
Zoom in on one single km.
Drag the top of each yellow step up until it touches its line.
That climb per step has a name.
How much a line climbs for one step to the right is its slope. Rocket's slope is 2, Comet's is 1.
Slope is a rate of change: here, dollars per km. A steeper line means a faster climb.
Over several steps, divide: slope = rise ÷ run. Rocket climbs $6 from 1 km to 4 km, and 6 ÷ 3 = 2.
Comet wants to earn more per km.
Turn the dial until Comet's line is exactly as steep as Rocket's.
Launch your own app: $3 to get in.
Drag the blue handle to set your price per km. Earn at least $1 per km, and be the cheapest on the 9 km ride.
Game: match the mystery lines.
Read each dashed line's slope from the grid, set it on the dial, then draw. Fewest tries wins.
Three AI models are training. Which one learns fastest?
Each line is a model's error after each training round. Lower error means a better model. Tap a line to see its slope.
This line passes through (1, 3) and (3, 7). What is its slope?
Slope is a rate: how much more for each step right.
Race your app against Comet and Rocket on the 9 km ride.

Lessons are interactive and need JavaScript. Turn it on to play them.