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

y = k x

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

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

The graph the the straight variation equation is a directly line with the origin.


direct Variation Equation

for 3 different values the k

example 1:

given that y varies straight as x , through a continuous of variation k = 1 3 , uncover y when x = 12 .

write the straight variation equation.

y = 1 3 x

instead of the provided x value.

y = 1 3 ⋅ 12 y = 4

instance 2:

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

compose the straight variation equation.

y = k x

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

24 = k ⋅ 3     k = 8

instance 3:

expect y varies directly 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 given x and 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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