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Direct variation describes a simple relationship between two variables . We say varies directly with (or as , in some textbooks) if:
for some constant , called the constant of variation or constant of proportionality . (Some textbooks describe direct variation by saying " varies directly as ", " varies proportionally as ", or " is directly proportional to .")
This means that as increases, increases and as decreases, decreases—and that the 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 different values of |
Example 1:
Given that varies directly as , with a constant of variation , find when .
Write the direct variation equation.
Substitute the given value.
Example 2:
Given that varies directly as , find the constant of variation if and .
Write the direct variation equation.
Substitute the given and values, and solve for .
Example 3:
Suppose varies directly as , and when . What is the value of when ?
Write the direct variation equation.
Substitute the given and values, and solve for .
The equation is . Now substitute and find .