Find the correct rule for the numbers in the table. When 𝑥 equals two, 𝑦 equals eight. When 𝑥 equals four, 𝑦 equals 16. When 𝑥 equals eight, 𝑦 equals 32. When 𝑥 equals 10, 𝑦 equals 40. A) Multiply 𝑥 by four to find 𝑦. B) Double 𝑦 to find 𝑥. C) Add two to 𝑥 to find 𝑦. D) Subtract two from 𝑥 to find 𝑦. Or E) Divide 𝑥 by four to find 𝑦.
So to solve this problem, what we’re going to do is go through each of our answers in turn to see if there is a possibility. So we’re gonna start with A. Multiply 𝑥 by four to find 𝑦. So if we start with the first term for 𝑥, which is 𝑥 equals two, if we multiply this by four, we get eight. So the first column is correct.
So then, for the second column, we have four. So four multiplied by four gives us 16. So this column is correct. So then, we’ll try the third column. Well, eight multiplied by four is 32. So again, this column is correct. So finally, we’ve got 𝑥 equals 10. So if we do 10 multiplied by four, we get 40. So we can see that actually each of these columns is correct and follows the rule multiply 𝑥 by four to find 𝑦. So therefore, this is the correct rule.
So what we’re gonna quickly do is check the other rules to see if any of those are possible as well. So we now take a look at B. Double 𝑦 to find 𝑥. So if we try the first column, where 𝑦 is equal to eight, and if we’re gonna double that, we do eight multiplied by two, which would be 16. So this is not equal to two. So we can say that this is not our rule.
So now, we can move on to answer C, which says add two to 𝑥 to find 𝑦. So we can start again with the first column. If we start with 𝑥 equal to two, well two add two is equal to four, which is not equal to eight where it should be because in the first column, it says 𝑦 is equal to eight. So therefore, we know that this will not be the rule.
So now we can check answer D. Well, answer D says subtract two from 𝑥 to find 𝑦. Well again, if we substitute in two because 𝑥 is equal to two and then we subtract two from two, we’re gonna get zero. Well, that’s not equal to eight because as we said 𝑦 is equal to eight in the first column. So again, this cannot be our rule.
So then, finally, we’ll check answer E, which says divide 𝑥 by four to find 𝑦. Well, if we try this one, we again look at the first column. We’ve got 𝑥 equal to two. So we do two divided by four, which would give us a half. Well again, this is not equal to eight.
So therefore, we can say that the only possible correct rule for the numbers in the table from the five answers that we have is multiply 𝑥 by four to find 𝑦. And that’s answer A.