direct variation describes a an easy relationship between two variables . We say y varies directly through x (or together x , in part textbooks) if:

y = k x

for part constant k , referred to as the continuous of variation or consistent of proportionality . (Some textbooks explain direct sport by saying " y varies directly as x ", " y different proportionally together x ", or " y is straight proportional to x .")

This means that together x increases, y increases and as x decreases, y decreases—and that the proportion between them always stays the same.

The graph the the direct variation equation is a straight line through the origin.

straight Variation Equation

because that 3 various values of k

example 1:

provided that y varies directly as x , with a constant of sports k = 1 3 , discover y as soon as x = 12 .

create the direct variation equation.

y = 1 3 x

instead of the offered x value.

y = 1 3 ⋅ 12 y = 4

instance 2:

given that y varies directly as x , discover the consistent of sports if y = 24 and also x = 3 .

create the direct variation equation.

y = k x

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

24 = k ⋅ 3     k = 8

example 3:

mean y varies directly as x , and y = 30 when x = 6 . What is the value of y as soon as x = 100 ?

write the direct variation equation.

y = k x

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

30 = k ⋅ 6     k = 5

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

y = 5 ⋅ 100 y = 500

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