A proportional connection is one in i beg your pardon two amounts vary straight with every other. Us say the change y varies directly as x if:

y = k x

for some consistent k , dubbed the consistent of proportionality .

(Some textbooks define a proportional relationship by saying the " y different proportionally through x " or that " y is straight proportional to x .")

This means that together x increases, y increases and as x decreases, y decreases-and that the ratio in between them constantly stays the same.

The graph that the proportional partnership equation is a straight line with the origin. example 1:

given that y different proportionally v x , through a consistent of proportionality k = 1 3 , find y once x = 12 .

create the equation the the proportional relationship.

The variable x varies proportionally v y v a constant of proportionality same to 1 3 .

So, instead of the offered x value. example 2:

given that y varies proportionally with x , discover the constant of proportionality if y = 24 and x = 3 .

create the equation that the proportional relationship.

y = k x

instead of the offered x and also y values, and solve for k .

24 = k ⋅ 3 k = 8

instance 3:

suppose y different proportionally v x , and y = 30 as soon as x = 6 . What is the value of y when x = 100 ?

compose the equation the the proportional relationship.

y = k x

substitute the given x and y values, and solve because that k .

30 = k ⋅ 6

k = 5

The equation is y = 5 x . Currently substitute x = 100 and find y .

y = 5 ⋅ 100 y = 500

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