Question

Determine if the set of ordered pairs represents direct or inverse variation and find the value of r given that k = 5:

(1/2, 20)
(1, 5)
(2, 5/4)

Answer 1

The given set of ordered pairs represents inverse variation. The value of r is 1.

Step-by-step explanation:

The given set of ordered pairs represents inverse variation. In inverse variation, as one variable increases, the other variable decreases, and vice versa. To determine the value of the constant of variation (r) given that k = 5, we can use the formula:

x * y = k

1. For the ordered pair (1/2, 20): (1/2) * 20 = 10, which is not equal to 5. Therefore, it doesn't satisfy the inverse variation.
2. For the ordered pair (1, 5): 1 * 5 = 5, which satisfies the inverse variation. So, we can use this pair to find the value of r.
3. Substituting the values in the formula, we get: 1 * 5 = r * 5
4. Simplifying the equation, we get: r = 1

Therefore, the set of ordered pairs represents inverse variation, and the value of r is 1.