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Katie is measured every year at her annual checkup. When she was $11$ , she was $57$ inches tall. When she was $12$ , she was $59$ inches tall. She just turned $13$ , and now she is $63$ inches tall. Is the relationship between Katie's age and her height a linear relationship? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$ Now, justify your answer. $\newline$ Choices: $\newline$ (A)Katie's height increased by the same amount each year. $\newline$ (B)Katie's height increased by a different amount each year. $\newline$ (C)Katie got taller every year. $\newline$ (D)Katie's age increased by $1$ every year.

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Experimental probability

Full solution

Q. Katie is measured every year at her annual checkup. When she was

11

, she was

57

inches tall. When she was

12

, she was

59

inches tall. She just turned

13

, and now she is

63

inches tall. Is the relationship between Katie's age and her height a linear relationship?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Now, justify your answer.

\newline

Choices:

\newline

(A)Katie's height increased by the same amount each year.

\newline

(B)Katie's height increased by a different amount each year.

\newline

(C)Katie got taller every year.

\newline

(D)Katie's age increased by

1

every year.

Calculate Change in Height: Calculate the change in height from age $11$ to $12$ . $\newline$ Change = Height at $12$ - Height at $11$ = $59$ inches - $57$ inches = $2$ inches.
Compare Yearly Changes: Calculate the change in height from age $12$ to $13$ . $\newline$ Change = Height at $13$ - Height at $12$ = $63$ inches - $59$ inches = $4$ inches.
Compare Yearly Changes: Calculate the change in height from age $12$ to $13$ . $\newline$ Change = Height at $13$ - Height at $12$ = $63$ inches - $59$ inches = $4$ inches. Compare the yearly changes to determine if they are the same. $\newline$ Year $11$ to $12$ : Increase = $2$ inches. $\newline$ Year $12$ to $13$ : Increase = $4$ inches. $\newline$ Since $2$ inches $13$ $4$ $4$ inches, the increases are not the same each year.

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