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Elijah got to invite $5$ friends to his $5$ th birthday party, $6$ friends to his $6$ th birthday party, and $7$ friends to his $7$ th birthday party. Is the relationship between the number of guests and Elijah's age a linear relationship? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$ Now, justify your answer. $\newline$ Choices: $\newline$ (A)The number of friends increased by the same amount each year. $\newline$ (B)Elijah's age increased by $1$ each year. $\newline$ (C)Elijah got to invite more friends as he got older. $\newline$ (D)The rate of change increased by $1$ each year.

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Add and subtract integers: word problems

Full solution

Q. Elijah got to invite

5

friends to his

5

th birthday party,

6

friends to his

6

th birthday party, and

7

friends to his

7

th birthday party. Is the relationship between the number of guests and Elijah's age a linear relationship?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Now, justify your answer.

\newline

Choices:

\newline

(A)The number of friends increased by the same amount each year.

\newline

(B)Elijah's age increased by

1

each year.

\newline

(C)Elijah got to invite more friends as he got older.

\newline

(D)The rate of change increased by

1

each year.

List Friends and Age: First, let's list the number of friends Elijah invited each year and his age: $\newline$ - Age $5$ : $5$ friends $\newline$ - Age $6$ : $6$ friends $\newline$ - Age $7$ : $7$ friends $\newline$ We need to check if the number of friends increases by the same amount each year.
Calculate Differences: Calculate the difference in the number of friends between each year: $\newline$ - From age $5$ to $6$ : $6 - 5 = 1$ $\newline$ - From age $6$ to $7$ : $7 - 6 = 1$ $\newline$ Both differences are $1$ , indicating a constant increase.
Identify Linear Relationship: Since the number of friends increases by $1$ each year, and Elijah's age also increases by $1$ each year, the relationship between the number of guests and Elijah's age is linear.

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