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

Answer:

$y = x+ 2$ ---- Archie

$y = \frac{3}{2}x + 3$ --- Bailey

$y = \frac{5}{4}x +2$ --- Coco

Step-by-step 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)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{14 - 2}{12 - 0}$

$m = \frac{12}{12}$

$m =1$

Archie's equation is:

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

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

$y = 1(x) + 2$

$y = x+ 2$

Bailey

$y = \frac{3}{2}x + 3$ --- 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)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{9.5 - 4.5}{6 -2}$

$m = \frac{5}{4}$

Coco's equation is:

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

$y = \frac{5}{4}(x - 2) + 4.5$

$y = \frac{5}{4}x - \frac{5}{2} + 4.5$

$y = \frac{5}{4}x - 2.5 + 4.5$

$y = \frac{5}{4}x +2$