Question

carter is hooked on a new book series, the galaxy. each book in the series is the same length and chronicles a different year in the waka galaxy. carter has cleared off the top shelf of his bookcase to leave room for each of the books as they come out.
there is a proportional relationship between the number of books on the shelf, x, and how much shelf space the books take up (in inches), y.

x (books)	y (inches)
11	11
13	13
16	16

what is the constant of proportionality? write your answer as a whole number or decimal.
\boxed{} inches per book

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using the first pair of values

Take \( x = 2 \) and \( y = 2 \). Then \( k=\frac{y}{x}=\frac{2}{2} = 1 \).

Step3: Verify with other pairs

• For \( x = 11 \) and \( y = 11 \): \( k=\frac{11}{11}=1 \).
• For \( x = 13 \) and \( y = 13 \): \( k=\frac{13}{13}=1 \).
• For \( x = 16 \) and \( y = 16 \): \( k=\frac{16}{16}=1 \).

All pairs give \( k = 1 \), so the constant of proportionality is consistent.

Answer:

1