Where Lines Start

Lesson 3 of 10 · 7 min · Free, no account needed

What you will learn

The intercept b is where a line starts on the y axis: the value at x = 0.
Change b and the line slides without tilting. Change the slope m and it tilts around its start.
Every straight line is y = mx + b: two numbers are the whole line.

Rocket raises its start price to $4. Still $2 per km.
Where will its new line go? Press and drag on the grid to draw your guess.
Turn Rocket's start knob until it matches the new price.
The dashed line is Rocket at $4 to get in. Watch what the line leaves behind as you turn.
Rocket wants to beat Comet on a 9 km ride, and keep its $4 start.
Try both knobs. Which one can win without breaking the $4 promise?
Two knobs, two names.
b, the intercept: where the line starts on the y axis, the value at x = 0. Rocket's b is 4.
m, the slope: how much the line climbs for each step right. Rocket's m is 2.
Together they make the whole line: y = mx + b. Rocket is y = 2x + 4. Turn b and it slides; turn m and it tilts.
Build each dashed line from tiles.
Fill y = mx + b. Your line is drawn live, so a wrong tile shows at once.
Launch a scooter app.
Drag the green start and the blue slope handle. Charge at least $1 per km, and beat Rocket on 2 km and Comet on 9 km.
Game: laser run.
Drag the laser's start on the y axis, set its slope, and Fire. One beam must pass through both targets.
An AI model sorts cats and dogs with a line.
Its slope is fixed. Drag the boundary up or down until every dog is above it and every cat is below.
Place the line y = 0.5x + 3.
Drag the two pins: one on the y axis, one at x = 4. The line goes through them.
Comet and Rocket copy your price per km.
Same slope for all three apps, different starts. Tap each ride length: who wins?

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