Respuesta :
The function that models the inverse variation is y=96/x. Thus, the correct option is A.
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.
Given that x and y vary inversely. Therefore, the relation can be written as,
y ∝ 1/x
y = k × 1/x
y = k/x
Also, when y =8, the value of x is 12, therefore, if we substitute the points in the above-formed equation,
y = k/x
8 = k /12
k = 96
Hence, the function that models the inverse variation is y=96/x. Thus, the correct option is A.
Learn more about Directly and Inversely proportional relationships:
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