Answer:
n = 17
Rule: y = 2x + 1
Step-by-step explanation:
By inspection of the first two ordered pairs in the given table, it appears that for each 1 unit increase in x, y increases by 2 units.
To check this, write the ordered pairs with 5 ≤ x ≤ 10 using this rule:
(5, 11) (6,13) (7, 15) (8, 17) (9, 19) (10, 21)
As the ordered pair (10, 21) appears in the table, then we can confirm that this is the rule and that it is a linear function.
If y increases by 2 units for every 1 unit increase of x, then the slope of the linear function will be 2.
Using the point-slope form of a linear function: [tex]\sf{y-y_1=m(x-x_1)}[/tex]
(where m is the slope and [tex]\sf(x_1,y_1)[/tex] is a point on the line)
Given:
- m = 2
- [tex]\sf(x_1,y_1)=(5,11)[/tex]
Substituting these values into the formula:
[tex]\implies \sf{y-11=2(x-5)}[/tex]
[tex]\implies \sf y=2x+1[/tex]
Therefore, the rule is [tex]\sf y=2x+1[/tex]
To find n, simply substitute x = 8 and y = n into the equation:
[tex]\implies \sf n=2(8)+1=17[/tex]
Therefore, n = 17
