In a directly proportional relationship, increasing one variable will increase another. The correct option is B, 17.
What is the directly proportional and inversely proportional relationship?
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
Let the relation between the number of Packs of Cereal and the number of Ounces of Cereal be directly proportional, then we can write,
Number of Ounces of Cereal ∝ Number of Packs of Cereal
Number of Ounces of Cereal = k × Number of Packs of Cereal
Substitute any one of the points from the table in the equation formed above,
34 = k × 2
k = 17
Hence, the constant of proportionality is 17.
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