Rate of change from a table, step by step
How much does y move for every ONE x?
x: 7, 12, 17, 22 y: 90, 65, 40, 15
- 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 −25, −25, −25. 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 −25 while x moved 5. Those two numbers are the whole of the division below.
- Now divide: −25 ÷ 5 = −5. This is the step that gets skipped — −25 is how far y went over 5 of them, not over one.
- The table starts at x = 7, not at 0, so the value there is not written down — step back to it. Going one x backwards adds 5 to y each time, and there are 7 to go.
- 90 + 35 = 125. So at x = 0 the value would be 125 — at x = 7 the value is 90, and stepping back 7 of them at −5 each gives 125.
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 −25, −25, −25. 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 −25 while x moved 5. Those two numbers are the whole of the division below.
- 04
Now divide: −25 ÷ 5 = −5. This is the step that gets skipped — −25 is how far y went over 5 of them, not over one.
- 05
The table starts at x = 7, not at 0, so the value there is not written down — step back to it. Going one x backwards adds 5 to y each time, and there are 7 to go.
- 06
90 + 35 = 125. So at x = 0 the value would be 125 — at x = 7 the value is 90, and stepping back 7 of them at −5 each gives 125.