Question

What is the rule and how do you find n? 100 points to answer!

Answer 1

Take 2 points and form equation

• (5,11)
• (6,13)

Slope:-

• m=13-11/6-5=2

Equation in point slope form

• y-11=2(x-5)
• y-11=2x-10
• y=2x+1

So

for n

• n=2(8)+1
• n=16+1
• n=17

Answer 2

n = 17

Rule: y = 2x + 1

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:
`\sf{y-y_1=m(x-x_1)}`

(where m is the slope and
`\sf(x_1,y_1)` is a point on the line)

Given:

• m = 2
• 
  `\sf(x_1,y_1)=(5,11)`

Substituting these values into the formula:

`\implies \sf{y-11=2(x-5)}`

`\implies \sf y=2x+1`

Therefore, the rule is
`\sf y=2x+1`

To find n, simply substitute x = 8 and y = n into the equation:

`\implies \sf n=2(8)+1=17`

Therefore, n = 17