Step by step
The question
Question: which grows faster: function A, y = 5x + 2, or function B, x: 1, 2, 3; y: 5, 9, 13?
A: y = 5x + 2
= B: x: 1, 2, 3; y: 5, 9, 13
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: 5.
= y = 5x + 2: m = 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
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
= 5 > 4 → A grows faster