### Video Transcript

If 𝑦 is proportional to one
divided by the square root of 𝑥, then which of the following is true? A) 𝑥 is inversely proportional to
𝑦 squared; B) 𝑥 is inversely proportional to 𝑦 cubed; C) 𝑥 is directly
proportional to 𝑦 squared; D) 𝑥 is directly proportional to 𝑦; or E) 𝑥 is
inversely proportional to 𝑦.

If we consider the question, 𝑦 is
proportional to one divided by the square root of 𝑥 is the same as saying 𝑦 is
inversely proportional to the square root of 𝑥. This will automatically rule out
answer C and answer D, as they refer to direct proportion. If 𝑦 is inversely proportional to
the square root of 𝑥, then 𝑥 must be inversely proportional when related to
𝑦.

We now need to alter the equation
𝑦 is proportional to one over square root of 𝑥 so that 𝑥 is the subject of the
equation. Squaring both sides of the equation
gives us 𝑦 squared is proportional to one divided by 𝑥. This is because the square root of
𝑥 multiplied by the square root of 𝑥 is 𝑥. Multiplying both sides of this
equation by 𝑥 gives us 𝑥𝑦 squared is proportional to one. And finally, dividing both sides by
𝑦 squared gives us that 𝑥 is proportional to one divided by 𝑦 squared, or one
over 𝑦 squared.

As 𝑥 is proportional to one over
𝑦 squared, we can say that 𝑥 is inversely proportional to 𝑦 squared. Answer A was true. If 𝑦 is proportional to one over
the square root of 𝑥, then 𝑥 is inversely proportional to 𝑦 squared.