Which grows faster: y = 3x + 1 or x 0, 1, 2; y 2, 6, 10

Step by step, with the reason for every step · Compare two functions · Algebra 1

Step by step

Question: which grows faster: function A, y = 3x + 1, or function B, x: 0, 1, 2; y: 2, 6, 10?

A: y = 3x + 1

= B: x: 0, 1, 2; y: 2, 6, 10

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

In y = m x plus b, m is the number in front of x: 3.

= y = 3x + 1: m = 3

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

4 is bigger.

So function B grows faster.

= 3 < 4 → B grows faster

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

= 3 < 4 → B grows faster

Try this one yourself, then check:

Which grows faster: function A, A: y = x

Show the answer

B grows faster