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Current time:0:00Total duration:4:31

Interpreting patterns on coordinate plane

CCSS.Math:

Video transcript

the following graph represents the first five terms of two given patterns in the answer box there are different statements about the two patterns choose all correct statements so here for each point this point right over here this represents its horizontal coordinate is the first term of pattern a which is four and it's a vertical coordinate is the first term in pattern B which is one and then we could do that for the other points as well so actually let's figure out what the values are so we have pattern a and then we have pattern B so the first term for pattern a is four and when pet that first when pattern a is for the first term for pattern B is one the second term for pattern a is 7 and when pattern a is 7 pattern B is also 7 third term pattern a is 10 and pattern B is 13 and then fourth term pattern a is pattern a is 13 and pattern B is 19 and then finally fifth term pattern a is 16 is 16 and pattern B and pattern B is 25 now before even looking at these let's see what we can think about these patterns here so it looks like pattern a starts at 4 and it increases by 3 every time to go from one term to the next you just have to add just have to add 3 now what about for pattern B well pattern B starts at 1 and every term here it looks like you're adding 6 when pattern a increases by 3 and we're moving in the horizontal direction the base based on the fact that pattern a is on represent on the horizontal axis we're going to move up 6 in the vertical axis and we see that here pattern a increases by 3 pattern a increases by 3 from one term to the next and when that increased by 3 pattern B increased by 6 from one term to the next pattern B increased by 6 from one term to the next and we see that it keeps it keeps it keeps doing that now let's think about what we have over here to see which of these statements actually apply to this for every term in pattern a multiply the term by 2 and then subtract 7 to get the corresponding term from pattern B so let's see with that let's see if that holds up so according to this if this was true I should be able take this multiplied by 2 and subtract 7 and get that so let's see is 1 equal to 2 times 8 minus 7 or sorry 2 times 4 minus 7 so 2 times this number 2 times 4 minus 7 well 8 minus 7 is equal to 1 is this right over here equal to 2 times this 7 minus 7 well yeah it's equal to 7 is 13 equal to 2 times 10 2 times 10 minus 7 yeah 20 minus 7 is 13 is 19 equal to 2 times 13 minus 7 26 minus 7 is 19 is 25 equal to 2 times 16 minus 7 well 32 minus minus 7 is 25 so this first statement checks out for the corresponding term the value of pattern B is 2 times the value of pattern a minus 7 now let's look at the second one the terms of pattern B are always greater than or equal to their corresponding terms from pattern a well no that's not right it's true for a couple of scenarios here for the third fourth and fifth term or actually for the second third and fourth second third fourth and fifth terms pattern B is equal to or greater than pattern a but for the first term it's not true pattern a is greater so this is not this is not right to get from each point to the next you need to move three units to the right and 6 units up well that's exactly what we talked about from one term to the next pattern a along our horizontal axis we increase by three while pattern B we increase which is plotted on our vertical axis by six so you move three to the right and six up so that is right the second terms of both patterns are 7 well yeah we see that right over here the second terms are 7 we have 7 here and we have seven there and so that is right as well so the only one that doesn't apply is this second one this is not right