Step by step
The question
Question: which grows faster: function A, line through (1, 2) and (3, 12), or function B, x: 0, 1, 2; y: 0, 4, 8?
A: line through (1, 2) and (3, 12)
= B: x: 0, 1, 2; y: 0, 4, 8
Rate of change means: how much y changes when x goes up by 1.
The bigger one grows faster.
grows faster = bigger rate of change
1 Rate of change of A
Between the two points: the change in y over the change in x.
That is 5.
= m = 12 − 23 − 1 = 5
2 Rate of change of B
In the table, y changes by 4 each time x goes up by 1.
So the rate of change is 4.
= changes: + 4, + 4 → m = 4
3 Compare
5 is bigger.
So function A grows faster.
= 5 > 4 → A grows faster
Careful!
Function B starts higher.
But it grows more slowly.
Careful: the higher start is not the faster one
4 Check
Let's check: both lines on one grid.
Line A is steeper: it climbs faster.
So the answer is right!
Let's look back.
First: rate of change of A.
Then: rate of change of B.
Then: compare.
Last: check.
Answer
Careful: the higher start is not the faster one