Step by step
The question
Question: which is steeper: function A, y = 7x − 3, or function B, line through (0, 0) and (2, 12)?
A: y = 7x − 3
= B: line through (0, 0) and (2, 12)
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: 7.
= y = 7x − 3: m = 7
2 Rate of change of B
Between the two points: the change in y over the change in x.
That is 6.
= m = 12 − 02 − 0 = 6
3 Compare
7 is bigger.
So function A grows faster.
= 7 > 6 → 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