Step by step
The question
Question: which grows faster: function A, line through (0, 3) and (2, 7), or function B, y = 3x?
A: line through (0, 3) and (2, 7)
= B: y = 3x
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
Between the two points: the change in y over the change in x.
That is 2.
= m = 7 − 32 − 0 = 2
2 Rate of change of B
In y = m x plus b, m is the number in front of x: 3.
= y = 3x: m = 3
3 Compare
3 is bigger.
So function B grows faster.
= 2 < 3 → 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