straight variation explains a straightforward relationship in between two variables . We say y varies straight v x (or together x , in some textbooks) if:

y = k x

for part consistent k , called the continuous of variation or consistent of proportionality . (Some textbooks describe direct sport by saying " y varies straight as x ", " y varies proportionally as x ", or " y is directly proportional come x .")

This way that as x increases, y increases and as x decreases, y decreases—and the the proportion between them constantly stays the same.

The graph of the direct variation equation is a directly line v the origin.


straight Variation Equation

because that 3 various values the k

instance 1:

provided that y varies straight as x , through a constant of sports k = 1 3 , uncover y once x = 12 .

compose the direct variation equation.

y = 1 3 x

substitute the given x value.

y = 1 3 ⋅ 12 y = 4

example 2:

offered that y varies straight as x , discover the consistent of sport if y = 24 and x = 3 .

create the direct variation equation.

y = k x

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

24 = k ⋅ 3     k = 8

example 3:

expect y varies straight as x , and y = 30 as soon as x = 6 . What is the value of y as soon as x = 100 ?

create the direct variation equation.

y = k x

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

30 = k ⋅ 6     k = 5

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

y = 5 ⋅ 100 y = 500

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