Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if:

y = k x

for some consistent k , called the constant of variation or constant of proportionality . (Some textbooks describe direct variation by saying " y varies directly together x ", " y varies proportionally as x ", or " y is directly proportional to x .")

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

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


Direct Variation Equation

for 3 different values that k

Example 1:

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

Write the direct variation equation.

y = 1 3 x

Substitute the given x value.

y = 1 3 ⋅ 12 y = 4

Example 2:

Given that y varies directly as x , find the constant of variation if y = 24 and also x = 3 .

Write the direct variation equation.

y = k x

Substitute the provided x and y values, and solve for k .

24 = k ⋅ 3     k = 8

Example 3:

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

Write the direct variation equation.

y = k x

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

30 = k ⋅ 6     k = 5

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

y = 5 ⋅ 100 y = 500

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