a. The table represents a proportional relationship
b. The constant of proportionality is 5/6
Proportional relationship are relationship between variable where their ratios are equivalent. The variables in our case are total weight(pounds) and number of books.
Therefore, let's check if the table represent a proportional relationship.
let
total weight = x
number of book = y
k = constant of proportionality
y = kx
10 = k12
k = 10 / 12 = 5 / 6
y = kx
15 = 18k
k = 15 / 18
k = 5 / 6
y = kx
25 = 30k
k = 25 / 30
k = 5 / 6
y = kx
50 = k60
k = 50/60 = 5 / 6
The constant of proportionality is the same. Therefore, the table represents a proportional relationship
The constant of proportionality(k) is 5/6.
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