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Interpreting relationships in ordered pairs

Video transcript
Below are ordered pairs that represent the first six terms of two given patterns. The first value in each pair is a term from pattern A. And the second value is a term from pattern B. In the answer box, there are different statements about the two patterns. Choose all correct statements. So let's think about what's going on here. They said the first term is pattern A. So the first term in each of these coordinates is pattern A, or in each pair is pattern A. So pattern A goes from 1, to 2, to 4, to 8, to 16, to 32. So it looks like pattern A, to go from the first term to the second term, we multiplied by 2. And then to go from the second to the third term, we also multiplied by 2. And we just keep multiplying by 2. And we just keep doing that. 8 times 2 is 16. 16 times 2 is 32. Now let's think about what's going on with pattern B. So pattern B is the second number in each of these pairs. And it's just always 3. So there's a couple of ways you can think about it. You could just say, pattern B's always 3. You could say pattern B starts at 3, and we're just adding 0 every time. Or you could say that pattern B starts at 3, and we are multiplying by 1 every time. Either of those would give you just 3 showing up over and over again. So now that we've looked at these pairs, we show the corresponding terms for pattern A and pattern B, let's look at the choices here and see which of these apply. In pattern A, you can get from any term to the next by multiplying by a constant number. Well, that looks right. We go from the first term to the second term by multiplying by 2. Then we multiply by 2 again to get to the third term. Then we keep multiplying by 2. So that constant number that we're multiplying by to get to the next term is 2. So this looks right. The next pair should be 52 comma 3. So let's think about this. If we keep doubling for pattern A-- so this is going to be times 2. 32 times 2 is 64. And then if we'd say that this is 1 times the previous term, we're just going to get a 3 again. So it should be 64 comma 3 should be the next one. They say the next pair should be 52 comma 3. So that's not right. If we graph the pairs, the points will be on the same line. So let's think about that a little bit. Let's think about that. So this is my vertical axis. This is my horizontal axis. On the horizontal axis, I will graph pattern A. And on my vertical axis, I will graph pattern B. And let's see. Pattern A goes all the way up to 32. So I'm going to try my best here. So let's say that this is 32. Then half of that is going to be 16. Half of that is going to be 8. Half of that is going to be 4. Half of that is going to be 2. And half of that is going to be 1. So these are all the points on pattern A. But for any of them, the corresponding term on pattern B is 3. So we have, when pattern A is 1, pattern B is 3-- 1,3. When pattern A is 2, pattern B is 3. When pattern A is 4, pattern B is 3. When pattern A is 8, pattern B is 3. When pattern A is 16, pattern-- this is like a tongue-- when pattern A is 16, pattern B is 3. When pattern A is 32, pattern B is 3. And you see, they all sit on a line. They all sit on this horizontal line, or at least the way that we've drawn it. They all sit on this line that you probably can't see in yellow. So let me do it in this red color. They all sit on this line right over here. So this looks right. If we graph the pairs, the points will be on the same line. So I'll go with that one. In pattern B, you can get from any term to the next by multiplying by a constant number. Well, yeah, even though every term is the same term, but you can get from a 3 to a 3 by always multiplying by 1. 1 is a constant number. So we're just multiplying every term by 1. So that also seems to be right. So all of these are right, except the second one. The next pair isn't 52 comma 3. It's going to be 64 comma 3.