How to solve the direct variation problem: definition, 2 examples, and their solutions.
The direct variation is a relation
whose ratio of the variables, y/x, is constant, m:
y/x = m.
m is the constant of variation.
From y/x = m, multiply x on both sides.
Then y = mx.
This y = mx is the formula
that shows the direct variation.
ExampleConstant of Variation
x varies directly as y means
x and y show direct variation.
find the constant of variation
by comparing y to x.
This means the constant of variation, m, is
x = 2, y = 8
So m = 8/2.
8/2 = 4
So the constant of variation is 4.
the formula between x and y is
y = 4x.
ExampleFind the y value
First find the constant of variation.
x = 2, y = 4
So the constant of variation, m, is 4/2.
4/2 = 2
So m = 2.
The constant of variation, m, is 2.
So write the formula of the relation:
y = 2x.
x = 5, y = k
Put these into the formula y = 2x.
Then k = 2⋅5.
2⋅5 = 10
So k = 10 is the answer.