Question

Mario's dog has three puppies: Archie, Bailey, and Coco. Mario measures the weight of the puppies across several months. Then he represents their weight as a function of time. In all three functions, represents each puppy's weight in pounds and x represents the time in months.

Answer 1

`y = x+ 2` ---- Archie

`y = (3)/(2)x + 3` --- Bailey

`y = (5)/(4)x +2` --- Coco

Explanation:

Given

See attachment for the representation

Required

Determine the function (i.e. equation) of each

Archie

Take 2 point from the line of the graph

`(x_1,y_1) = (0,2)`

`(x_2,y_2) = (12,14)`

Calculate slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (14 - 2)/(12 - 0)`

`m = (12)/(12)`

`m =1`

Archie's equation is:

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

`y = 1(x - 0) + 2`

`y = 1(x) + 2`

`y = x+ 2`

Bailey

`y = (3)/(2)x + 3` --- Given

Coco

Take 2 point from the table

`(x_1,y_1) = (2,4.5)`

`(x_2,y_2) = (6,9.5)`

Calculate slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (9.5 - 4.5)/(6 -2)`

`m = (5)/(4)`

Coco's equation is:

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

`y = (5)/(4)(x - 2) + 4.5`

`y = (5)/(4)x - (5)/(2) + 4.5`

`y = (5)/(4)x - 2.5 + 4.5`

`y = (5)/(4)x +2`