Step by step
The question
Question: which grows faster: function A, y = 4x − 2, or function B, line through (0, 1) and (2, 11)?
A: y = 4x − 2
= B: line through (0, 1) and (2, 11)
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: 4.
= y = 4x − 2: m = 4
2 Rate of change of B
Between the two points: the change in y over the change in x.
That is 5.
= m = 11 − 12 − 0 = 5
3 Compare
5 is bigger.
So function B grows faster.
= 4 < 5 → B grows faster
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
= 4 < 5 → B grows faster