Initial value from a table, step by step
The initial value is y when x is 0 — and these tables never print that row.
x: 9, 14, 19, 24 y: 73, 108, 143, 178
- Rate of change means how much y moves for every ONE x. So it is a division, and the two things being divided are both differences: how far y went, over how far x went.
- Take both rows of steps. x moves 5, 5, 5 — the same each time — and y moves 35, 35, 35. They are steady, so this table really does have one rate rather than a different one in every gap.
- Written out, that is one step of each: y moved 35 while x moved 5. Those two numbers are the whole of the division below.
- Now divide: 35 ÷ 5 = 7. This is the step that gets skipped — 35 is how far y went over 5 of them, not over one.
- The table starts at x = 9, not at 0, so the value there is not written down — step back to it. Going one x backwards takes 7 off y each time, and there are 9 to go.
- 73 − 63 = 10. So at x = 0 the value would be 10 — at x = 9 the value is 73, and stepping back 9 of them at 7 each gives 10.
How it works.
- 01
Rate of change means how much y moves for every ONE x. So it is a division, and the two things being divided are both differences: how far y went, over how far x went.
- 02
Take both rows of steps. x moves 5, 5, 5 — the same each time — and y moves 35, 35, 35. They are steady, so this table really does have one rate rather than a different one in every gap.
- 03
Written out, that is one step of each: y moved 35 while x moved 5. Those two numbers are the whole of the division below.
- 04
Now divide: 35 ÷ 5 = 7. This is the step that gets skipped — 35 is how far y went over 5 of them, not over one.
- 05
The table starts at x = 9, not at 0, so the value there is not written down — step back to it. Going one x backwards takes 7 off y each time, and there are 9 to go.
- 06
73 − 63 = 10. So at x = 0 the value would be 10 — at x = 9 the value is 73, and stepping back 9 of them at 7 each gives 10.