Linear Functions & Rate
📋 What it is
A linear function graphs as a straight line; its rate of change (slope) is constant.
🗣️ Coach says
A linear function grows by the same amount every step — so its graph is a straight line. That steady amount is the slope (rate of change). "$2 per item" is linear: the cost climbs $2 each time.
🧠 Memory hook
Linear = straight line = SAME jump every step. That constant jump is the slope.
😂 Giggle
Why did the pattern feel proud?
Because it was totally predictable — and that's a good thing in math!
😲 Whoa!
A phone plan with a flat monthly fee plus a per-minute rate is a linear function you pay every month.
✅ Quick check: A function goes up by 2 for every step of 1 in x. What is its rate of change (slope)?
Say your answer out loud first — then reveal.
2 — the output rises 2 for each 1 increase in input.
Slope is the constant change in output per unit change in input.
🧪 Try it! (2 minutes)
Track a "3 per step" pattern: 3, 6, 9, 12. The steady +3 is the slope.