Mothergoosiferidn
Answered

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does the relationship in the table represent direct variation, inverse variation, or neither? If it is direct of inverse variation, write an equation to represent the relation. Explain your answer.

x = 5, 10, 15, 20

y = 2, 1, 1/3, 1/2

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Connexus

Sagot :

Answer:

The relationship in the table represents neither direct variation or inverse variation

Step-by-step explanation:

The table data are;

x = 5, 10, 15, 20

y = 2, 1, 1/3, 1/2

For a direct variation, we have;

y = k × x

Where;

k = A constant

Therefore;

k = y/x = constant for a direct variation

From the data, we have the following y/x values at each data point;

5/2 = 2.5

10/1 = 10

15/(1/3) = 45

20/(1/2) = 40

Therefore, y/x is not constant for the given data, therefore, the relationship in the table is not a direct variation

For an inverse variation, we have;

y·x = k (A constant)

The product of the 'x' and 'y' variables are given as follows;

5 × 2 = 10

10 × 1 = 10

15 × 1/3 = 5

20 × 1/2 = 10

The value of x × y is not always constant, therefore, therefore the relation in the table does not represent an inverse relation

Therefore, the relationship in the table represents neither direct variation or inverse variation

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Bilaal6090idn

The relation represents an inverse variation because as the values of x is increasing the values of y is decreasing.

y = k/x

5 = k/2

k = 5 x 2 = 10

So here K will be 10.

The given values are in inverse variation and can be represented by equation y = 10/x

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