Let’s Start With a Story
Imagine you work at a café and earn $15 per hour. The more hours you work, the more money you make. Simple, right?
That relationship — where one thing changes steadily based on another — is exactly what a linear function describes.
So What is a Linear Function?
A linear function is a relationship between two things that changes at a constant rate.
In math, it looks like this:
y = mx + b
But don’t let that scare you. Here’s what it means:
| Symbol | Meaning | Café Example |
|---|---|---|
| y | The result | Total money earned |
| x | The input | Hours worked |
| m | The rate of change | $15 per hour |
| b | The starting point | $0 (if you haven’t worked yet) |
So for our café example: y = 15x + 0
Work 3 hours → earn $45. Work 8 hours → earn $120. Easy!
What Makes it “Linear”?
When you plot a linear function on a graph, it always makes a straight line — that’s where the name comes from!
Real Life Examples
- 🚗 Driving — travel 60km every hour → distance = 60 × hours
- 💧 Filling a tank — add 5 litres per minute → total = 5 × minutes
- 📱 Phone plan — $10 base + $0.05 per text → cost = 0.05x + 10
Key Takeaway
A linear function is any relationship where one thing increases (or decreases) at a steady, consistent rate.
If you can describe something as “for every X, Y changes by the same amount” - that’s a linear function!