How to Find Constant of Proportionality?

A step-by-step guide to finding the constant of proportionality

1. Direct variation: The equation of direct proportionality is \(y = kx\), which shows that as \(x\) increases, \(y\) also increases at the same rate. Example: the cost of each item \((y)\) is directly proportional to the number of items \((x)\) purchased, expressed as \(y ∝ x\).
2. Inverse variation: The indirect proportionality equation is \(y= \frac{k}{x}\), which shows that as \(y\) increases, \(x\) decreases and vice versa. Example: the speed of a moving vehicle \((y)\) inversely varies as the time taken \((x)\) to travel a certain distance, expressed as \(y ∝ \frac{1}{x}\).

• Adjusting the ratio of ingredients in the recipe
• A quantifying chance like finding the odds and probability of events
• Scaling a diagram for design and architectural applications
• Finding percent increase or percent decrease for price mark-ups
• Discount products based on unit rate

How to solve the constant of proportionality?

Find Constant of Proportionality – Example 1:

First, find the ratio of \(x\) and \(y\) for all the given values.

\(\frac{2 }{1} = 2\)

\(\frac{4}{2} = 2\)

\(\frac{8}{4} = 2\)

When we take the ratio of \(x\) and \(y\) for all the given values, we get equal values for all the ratios. So, the relationship shown in the table is proportional.

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Exercises for Finding Constants of Proportionality

Examine each table and determine if the relationship is proportional.

1. \(\color{blue}{Not}\)
2. \(\color{blue}{Yes}\)

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