Step by step
The question
Question: which grows faster: function A, y = 6x, or function B, x: 0, 1, 2; y: 1, 3, 5?
A: y = 6x
= B: x: 0, 1, 2; y: 1, 3, 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: 6.
= y = 6x: m = 6
2 Rate of change of B
In the table, y changes by 2 each time x goes up by 1.
So the rate of change is 2.
= changes: + 2, + 2 → m = 2
3 Compare
6 is bigger.
So function A grows faster.
= 6 > 2 → 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