Pattern A: +3 each step; Pattern B: +6 each step
Two friends save money each week. Anna saves three dollars; Ben saves six dollars. Let's compare their savings.
Pattern A is Anna's savings: zero, three, six, nine, twelve. We add three each step.
Pattern B is Ben's savings: zero, six, twelve, eighteen, twenty-four. We add six each step.
Now let's line up matching terms from each pattern and look closely.
Look! Three times two is six. Six times two is twelve. Each B-term is double its A-partner.
We can pair each A-value with its B-value: zero-zero, three-six, six-twelve, nine-eighteen, twelve-twenty-four.
Now let's graph these pairs. The x-axis shows pattern A; the y-axis shows pattern B.
Plot three-six. Go three right, then six up, and drop the point.
Plot the rest: six-twelve, nine-eighteen, and twelve-twenty-four.
All five points sit on a straight line through zero. That's the picture of the rule!
Pattern B is always two times Pattern A. The graph rises twice as fast as it runs.