Graphing patterns on coordinate plane

the following table contains the first five terms of 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 three and add one to get the corresponding term of pattern B then graph the pairs of corresponding terms so every for every term in pattern a we want to multiply by three and add one so if we multiply 0 by 3 we get 0 and you add 1 you get 1 you multiply one 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 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 it's 1/4 so when pattern a is 1 pattern B is 4 pattern B on the vertical axis when pattern a is 2 pattern B is 7 so 2 & 7 when pattern a is 3 pattern B is 10 so 3 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 when pattern a is 4 pattern B is 13 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 its well pattern a starts at 0 and increases by one while pattern B starts at 1 increases and increases by three which makes complete sense it makes sense it starts at one because all of these you multiply by three and add one so you start at one and then the fact that we're multiplying by three that's what's leading to the distance between these points being three so let's check our answer make sure we got this we got this right and we did