Finding the rate of change, step by step
How much does y move for every one x?
The question
x471013y109825528rate
x: 4, 7, 10, 13 y: 109, 82, 55, 28
x471013y109825528
x steps333y steps−27−27−27
y step = −27x step = 3
−27÷3=−9
rate of change= −9
- 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 3, 3, 3 — the same each time — and y moves −27, −27, −27. 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 −27 while x moved 3. Those two numbers are the whole of the division below.
- Now divide: −27 ÷ 3 = −9. This is the step that gets skipped — −27 is how far y went over 3 of them, not over one.
- So the rate of change is −9: y moves −27 while x moves 3, and −27 ÷ 3 = −9.
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 3, 3, 3 — the same each time — and y moves −27, −27, −27. 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 −27 while x moved 3. Those two numbers are the whole of the division below.
- 04
Now divide: −27 ÷ 3 = −9. This is the step that gets skipped — −27 is how far y went over 3 of them, not over one.
- 05
So the rate of change is −9: y moves −27 while x moves 3, and −27 ÷ 3 = −9.