Question

Assume that y varies inversely with x. If y = 7 when x = 2/3, find y when x = 7/3.
y = [?] ​

Answer 1

y = 2

Explanation:

varies inversely

xy = k

y = 7 when x = 2/3

(2/3)7 = k

14/3 = k

k = 14/3

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find y when x = 7/3

(7/3)y = 14/3

multiply both sides by 3/7

y = 14/3 * 3/7

y = 2

Answer 2

Answer: y = 2

Step-by-step explanation: When we have two sets of inversely related coordinates, x₁ and y₁, and x₂ and y₂, we can use the product rule, shown below, to find the missing value.

x₁y₁ = x₂y₂

Since we know that y = 7 when x = 2/3, one set of coordinates will be 7 and 2/3 and since we want to find the value of y when x = 7/3, our other coordinates will be 7/3 and y.

(2/3)(7) = (7/3)(y)

So we have 14/3 = 7/3y and solving for y from here, we find that y = 2.