Question

What value of y would make {(-2, 18), (3, y), (6, 6), (-18, 2), (4, 9)} an inverse variation?​

Answer 1

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)}.