🧱 See It
In a discrete relation like weekly savings, "week 2.5" means nothing — only whole weeks are real. Now consider a car traveling at a steady 60 km/h. At exactly 1.5 hours, the car really has traveled a real, meaningful distance: 90 km. Every value in between the whole-number hours is just as meaningful as the whole numbers themselves. This is a continuous relation.
✏️ Draw It
Plot "hours" along the bottom and "distance" up the side for y = 60x. This time the line is drawn solid, because every point along it — not just the marked ones — is real data:
The line is solid because every value in between (like 1.5 hours → 90 km) represents a real, meaningful distance — not just a guide connecting separate dots.
🔢 Write It
Same equation format as a discrete relation:
y = 60x
But now it's interpreted continuously — any value of x at all, not just whole numbers, gives a meaningful y.
💡 Worked Examples
Example 1 — Find the distance at x = 2.5 hours:
- Use the rule:
y = 60x - Substitute:
y = 60 × 2.5 - Answer:
y = 150 km
Example 2 — Why "week 2.5" is different:
- For the weekly-savings relation, a deposit either happened at the end of a week or it hasn't happened yet — there's no such thing as half a week's deposit existing on its own.
- But for distance over time, the car is somewhere on the road at every instant, so "2.5 hours" is a real moment with a real distance.
- Answer: distance-over-time is continuous; weekly savings is discrete — the difference is about the real-world context, not the math itself.