# Question Video: Creating Inverse Variation Equations Mathematics • 9th Grade

Given that π varies inversely with π, and π = 5 when π = 3/4, write an equation for π in terms of π.

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### Video Transcript

Given that π varies inversely with π and π equals five when π equals three-quarters, write an equation for π in terms of π.

In this question, we are told that a variable π varies inversely with variable π and that when π is equal to five, we have that π is equal to three-quarters. We want to use this to find an equation for π in terms of π. To do this, we first recall that we say a variable varies inversely with another variable if it varies proportionally to its reciprocal. So, we must have that π is proportional to one over π. We can then recall that this is the same as saying that π is equal to π divided by π for some constant π, where π is nonzero. We call π the constant of proportionality.

To find an equation involving π and π, we need to find the value of π. We can do this by substituting the known values of π and π into this equation. Substituting π equals five and π equals three-quarters into the equation gives us five equals π divided by three-quarters. We can solve for π by multiplying both sides of the equation by three-quarters. We get π equals five times three-quarters, which we can evaluate is equal to 15 over four. We can now substitute π equals 15 over four into our proportionality equation to obtain that π equals 15 over four divided by π. This is an equation for π in terms of π.

We could leave our answer like this. However, we can simplify the equation by noting that instead of dividing by π, we can multiply by the reciprocal of π. This gives us that π is equal to 15 over four multiplied by one over π, which we can simplify to give us the equation π equals 15 over four π.