Question

Write and equation to represent the function.

Input(x). 1. 2. 3. 4
Output(y). 8. 19. 30. 41

Answer 1

`y=11x-3`

Explanation:

Given ordered pairs:

(1, 8) (2, 19) (3, 30) (4, 41)

As the y is directly proportional to x (y values increase +11 for every +1 increase for the x-values) then the equation will be linear.

Point-slope form of a linear equation:
`y-y_1=m(x-x_1)`

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

`\textsf{slope }m=(y_2-y_1)/(x_2-x_1)`

Let:

• 
  `(x_1,y_1)=(1,8)`
• 
  `(x_1,y_2)=(2,19)`

`\implies \textsf{slope }m=(19-8)/(2-1)=11`

Using point-slope equation with m = 11 and point (1, 8):

`y-y_1=m(x-x_1)`

`\implies y-8=11(x-1)`

`\implies y=11x-3`