Step by step
The question
Question: which grows faster: function A, y = x + 9, or function B, x: 0, 2, 4; y: 1, 5, 9?
A: y = x + 9
= B: x: 0, 2, 4; y: 1, 5, 9
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
In y = m x plus b, m is the number in front of x: 1.
= y = x + 9: m = 1
2 Rate of change of B
In the table, y changes by 4 each time x goes up by 2.
So the rate of change is 2.
= changes: + 4, + 4 for 2 of x → m = 2
3 Compare
2 is bigger.
So function B grows faster.
= 1 < 2 → B grows faster
Careful!
Function A 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 B 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