Question

caroline adopted a puppy named dodger from an animal shelter in chicago and recorded dodgers weight during the first two months. the data in the graph show dodgers weight \\(y\\) (in lb), \\(x\\) days after adoption.

part 1 of 5
(a) use the points \\((12, 14.3)\\) and \\((52, 24.7)\\) to write a linear model for these data.

\\(y = 0.26x + 11.18\\)

part 2 of 5
(b) interpret the meaning of the slope in context.
the slope of 0.26 means that dodgers weight increased by 0.26 lb per day during this period.

part 3 of 5
(c) interpret the meaning of the \\(y\\)-intercept in context.
the \\(y\\)-intercept is \\((\square, \square)\\) and indicates that dodgers weight when he was adopted was \\(\square\\) lb.

Explanation:

Step1: Identify the \(y\)-intercept from the linear model

\[y = 0.26x + 11.18\]

Step2: Write the \(y\)-intercept as an ordered pair

\[(0, 11.18)\]

Step3: Interpret the \(y\)-intercept in context

\[x = 0 \text{ represents the day of adoption.}\]

Step4: Determine the weight at adoption

\[y = 11.18 \text{ lb}\]

Answer:

The \(y\)-intercept is \((0, 11.18)\) and indicates that Dodger's weight when he was adopted was \(11.18\) lb.