Answer:
[tex]n=13[/tex]
Step-by-step Explanation:
In the table shown, [tex]y=2x+1[/tex] is how one would represent the behavior shown by the givens. In every single one of the [tex]x[/tex]-[tex]y[/tex] relationships given above, the [tex]y[/tex] value is equal to taking the corresponding [tex]x[/tex] value, multiplying it and adding [tex]1[/tex]. Thus, if we were to take our [tex]x[/tex] value, [tex]6[/tex], and plug it into our equation:
[tex]y=2x+1\\y=2(6)+1\\y=13[/tex]
[tex]n=13[/tex]
Extra Help + Tips:
Finding patterns and rules is a bit difficult to grasp if it is not taken in chunks. In this case, I saw that every given [tex]y[/tex] value was a little more than [tex]2[/tex] times the [tex]x[/tex] value, figured out the difference, [tex]1[/tex], and checked with every relationship to make sure that the rule that I found was correct. "Start with the order of operations and backsolve from there" is the way that I learned to find patterns, but if your teacher wants your class to find patterns in a specific way or by using a specific method, use it before using mine. A few tips:
- Try looking for a relationship between the smallest and largest values of the table, what gave me a big hint on the rule for this table was seeing how both small numbers and large numbers differed in the relationship between [tex]y[/tex] and [tex]x[/tex].
- Don't use complicated operations to solve tables. In most cases addition, subtraction, division and multiplication are all you need for finding the rule.
Hope this helped :)
