A proportional relationship is one in which 2 quantities differ straight through each various other. We say the variable y varies straight as x if:

y = k x

for some consistent k , dubbed the constant of proportionality .

(Some textbooks define a proportional connection by saying that " y varies proportionally with x " or that " y is directly proportional to x .")

This indicates that as x increases, y boosts and as x decreases, y decreases-and that the ratio in between them constantly remains the exact same.

The graph of the proportional connection equation is a directly line with the beginning. Example 1:

Given that y varies proportionally with x , via a continuous of proportionality k = 1 3 , find y when x = 12 .

Write the equation of the proportional partnership.

The variable x varies proportionally via y with a consistent of proportionality equal to 1 3 .

So, Substitute the given x worth. Example 2:

Given that y varies proportionally through x , uncover the continuous of proportionality if y = 24 and also x = 3 .

Write the equation of the proportional relationship.

y = k x

Substitute the provided x and also y worths, and also resolve for k .

24 = k ⋅ 3 k = 8

Example 3:

Suppose y varies proportionally via x , and also y = 30 as soon as x = 6 . What is the value of y as soon as x = 100 ?

Write the equation of the proportional relationship.

y = k x

Substitute the given x and y worths, and also settle for k .

30 = k ⋅ 6

k = 5

The equation is y = 5 x . Now substitute x = 100 and discover y .

y = 5 ⋅ 100 y = 500

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