Answer:
The value of "y" the would make the ordered pairs an inverse variation is;
y = 12
Step-by-step explanation:
The given ordered pairs are;
{(-2, 18), (3, y), (6, 6), (-18, 2), (4, 9)}
When a pair of variables, "x" and "y", vary inversely to one another, as the value of one variable increases, the value of the other variable decreases
Mathematically, we have;
y ∝ 1/x
The above relation can be represented as an equation as follows;
y = k/x
Where;
k = The constant of proportionality
Therefore, k = y·x
From the given ordered, we have;
k = -2 × 18 = -36
k = 6 × 6 = 36
k = -18 × 2 = -36
k = 4 × 9 = 36
Therefore, the value of "k" is made constant as follows;
The inverse variation is y = k/(x × (-1)ⁿ)
Where;
n = The number of the term
Therefore, y = 36/(3 × (-1)²) = 12
y = 12
The given ordered pairs can therefore be written as follows;
{(-2, 18), (3, 12), (6, 6), (-18, 2), (4, 9)}.
