Video: Finding the Constant of Proportionality

If 𝑦 ∝ π‘₯ and 𝑦 = 14 when π‘₯ = 6, determine the constant of proportionality.

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Video Transcript

If 𝑦 varies directly with π‘₯ and 𝑦 equals 14 when π‘₯ equals six, determine the constant of proportionality.

A direct variation is a relationship in which the ratio of 𝑦 to π‘₯ is a constant π‘˜. We say 𝑦 varies directly with π‘₯, so this constant of proportionality that we need to find is π‘˜.

And it says to find it when 𝑦 is equal to 14 and π‘₯ is equal to six, so let’s put those in. So we replaced 𝑦 with 14 and π‘₯ with six. So to solve for π‘˜, we need to divide both sides by six. The sixes cancel on the right-hand side.

Fourteen-sixths is equal to π‘˜, but fourteen-sixths reduces. Since two goes into 14 and six, π‘˜ will be equal to seven-thirds, because two goes into 14 seven times and two goes into six three times.

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