About this video
Pattern A is 0, 1, 2, 3, 4. The rule 'multiply by 3 and add 1' gives Pattern B: 1, 4, 7, 10, 13. The video graphs the pairs with Pattern A on the horizontal axis and Pattern B on the vertical axis, and notices that A goes up by 1 while B starts at 1 and goes up by 3 each time.
You'll be able to
- use a rule to make a second pattern from a first one.
- graph pairs of corresponding terms as points on a coordinate plane.
- explain how the rule shows up in the graph.
Key words
- pattern
- A list of numbers that follows a rule.
- term
- One number in a pattern.
- corresponding terms
- Terms in the same position in two patterns, like the first term of A and the first term of B.
- rule
- The instructions for making the numbers, such as 'multiply by 3 and add 1'.
Transcript
The following table contains the first five terms of the given Pattern A. Generate Pattern B according to this rule. For every term of Pattern A-- so they give us the terms of Pattern A here-- multiply the term by 3 and add 1 to get the corresponding term of Pattern B. Then graph the pairs of corresponding terms.
So for every term in Pattern A, we want to multiply by 3 and 1. So if we multiply 0 by 3, we get 0. And you add 1, you get 1. If you multiply 1 by 3, you get 3. And then you add 1, you get 4. 2 times 3 is 6, plus 1 is 7. 3 times 3 is 9, plus 1 is 10. Remember, we're just multiplying by 3 and adding 1.
4 times 3 is 12, plus 1 is 13. So those are the corresponding terms for Pattern B. And then they ask us to graph them. So let's try to graph these points. So when Pattern A is 0, Pattern B is 1. When Pattern A is 0-- so this is Pattern A equaling 0. That's our horizontal axis, the value of Pattern A-- Pattern B is the value of our vertical axis.
Pattern B is 1. When Pattern A is 1, Pattern B is 4. So when Pattern A is 1, Pattern B is 4. Pattern B is on the vertical axis. When Pattern A is 2, Pattern B is 7. When Pattern A is 3, Pattern B is 10, so 3 in the horizontal direction. That's our Pattern A value.
And our Pattern B value is 10. And then, finally, when Pattern A is 4, Pattern B is 13. Now, let's just look at these patterns. We see Pattern A is increasing by 1 each time, while Pattern B is increasing by it's-- well, Pattern A starts at 0 and increases by 1, while Pattern B starts at 1 and increases by 3, which makes complete sense.
It makes sense that it starts at 1, because all of these, you multiply by 3 and add 1. So you start at 1. And then, the fact that we're multiplying by 3, that's what's leading to the distance between these points being 3. So let's check our answer to make sure we got this right, and we did.
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