A slope is a rate. A zero is an x-value — and it may or may not mean anything.
A rate needs two units joined by per. An amount needs one.
For y = 2x − 6 the zero is 3 and the y-intercept is −6. Giving the same number twice is the commonest slip on the paper.
Same mathematics, same steps. Only you can tell which is which, because only you know what x stands for. A zero of 0 is not automatically meaningless either — judge every case on its own.
| Given | What to do | Example |
|---|---|---|
| A graph | rise ÷ run, between two exact grid points | up 6, across 2 → 3 |
| An equation | the number multiplying x — once it is in y = form | 3y = 9x + 6 → 3 |
| A table | change in y ÷ change in x | Δy 6, Δx 2 → 3 |
Three routes, one number. If the three do not agree, one of them was read wrong — that is a free check, and it costs a few seconds.
| x | 0 | 4 | 8 | 12 |
|---|---|---|---|---|
| y | 50 | 38 | 26 | 14 |
x almost never goes up by one in an examination table. Divide by Δx every time, even when Δx is 1.
That is a complete answer, not giving up. The number is correct and the situation is impossible.
Inventing a meaning for an impossible answer is the real mistake.