Step by step
The question
Question: which grows faster: function A, y = 10x + 1, or function B, y = 12x − 5?
A: y = 10x + 1
= B: y = 12x − 5
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: 10.
= y = 10x + 1: m = 10
2 Rate of change of B
In y = m x plus b, m is the number in front of x: 12.
= y = 12x − 5: m = 12
3 Compare
12 is bigger.
So function B grows faster.
= 10 < 12 → 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 at x = 10: A gives 101 and B gives 115.
B is bigger.
So the answer is right!
x = 10: A = 101, B = 115
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