WRITE DIRECT VARIATION EQUATIONS

Example 1 :

In a direct variation y = 12 when x = 2. Write the direct variation equation that shows the relationship between x and y.

Solution :

Equation of direct variation :

y  =  kx -----(1)

Substitute x = 2 and y = 12.

12  =  k(2)

12  =  2k

Divide each side by 2.

6  =  k

Substitute k = 1 in (1)

y  =  6x

Example 2 :

In a direct variation y = 300 when x = 5. Write the direct variation equation that shows the relationship between x and y .

Solution :

Equation of direct variation :

y  =  kx -----(1)

Substitute x = 5 and y = 300.

300  =  k(5)

300  =  5k

Divide each side by 5. 

60  =  k

Substitute k = 60 in (1). 

y  =  60x

Example 3 :

In a direct variation y = 12 when x = 40. Write the direct variation equation that shows the relationship between x and y .

Solution :

Equation of direct variation :

y  =  kx -----(1)

Substitute x = 40 and y = 12.

40  =  k(12)

40  =  12k

Divide each side by 12.

10/3  =  k

Substitute k = 10/3 in (1). 

y  =  (10/3)x

Example 4 :

In a direct variation y = 4 when x = 15. Write the direct variation equation that shows the relationship between x and y .

Solution :

Equation of direct variation :

y  =  kx -----(1)

Substitute x = 15 and y = 4. 

4  =  k(15)

4  =  15k

Divide each side by 15.

4/15  =  k

Substitute k = 4/15 in (1). 

y  =  (4/15)x

Example 5 :

In a direct variation y = 48 when x = 16. Write the direct variation equation that shows the relationship between x and y .

Solution :

Equation of direct variation :

y  =  kx -----(1)

Substitute x = 16 and y = 48. 

48  =  k(16)

48  =  16k

Divide each side by 16.

3  =  k

Substitute k = 3 in (1).

y  =  3x

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