A slope is a rate — and a rate has a unit
| A car goes 240 km in 3 hours | 80 kilometres per hour |
| 3 kg of rice costs ₱180 | 60 pesos per kilogram |
| A jeepney does 96 km on 8 litres | 12 kilometres per litre |
If a learner says just “80” — ask “eighty what?” and wait.
| Distance (km) | 0 | 1 | 2 | 5 |
|---|---|---|---|---|
| Fare (₱) | 30 | 42 | 54 | 90 |
It is not in the table. Let them hunt before you say so.
Two numbers. They are not the same kind of thing.
It means nothing. The number is correct and the situation is impossible. That is a complete answer, and you are allowed to give it.
| Write the equation | y = 200 − 25x |
| What is the slope? | −25 — negative, it falls |
| Its unit? | litres per minute |
| Find the zero | 200 − 25x = 0, so x = 8 |
| What does 8 mean? | The drum is empty after 8 minutes |
| Zero | What it means | |
|---|---|---|
| Tricycle y = 12x + 30 | −2.5 | nothing |
| Drum y = 200 − 25x | 8 | empty after 8 minutes |
Only you can tell which — because only you know what x stands for.
| Context | Equation | Slope | Zero | Meaning |
|---|---|---|---|---|
| Candle 24 cm, burns 3 cm per hour | y = 24 − 3x | −3 cm per hour | 8 | gone after 8 hours |
| Load ₱150, ₱2.50 per minute | y = 150 − 2.5x | −2.50 pesos per minute | 60 | used up after 60 minutes |
| Wage ₱80 per hour | y = 80x | 80 pesos per hour | 0 | no hours worked, no pay |
“Per what?”
And that one does mean something — no hours worked, no pay. So a zero of zero is not automatically meaningless either. Every case is judged on its own.
Quarter sheet. Name at the top. Read the unit in item 2 before anything else — a blank there is the whole lesson missing, however good the rest looks.