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Writing Direct Variation Equations Worksheet


Query 1 :

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

Query 2 :

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

Query 3 :

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

Query 4 :

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

Query 5 :

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

Solutions

1. Reply :

Equation of direct variation :

y  =  kx —–(1)

Substitute x = 2 and y = 12.

12  =  ok(2)

12  =  2k

Divide all sides by 2.

6  =  ok

Substitute ok = 1 in (1)

y  =  6x

2. Reply :

Equation of direct variation :

y  =  kx —–(1)

Substitute x = 5 and y = 300.

300  =  ok(5)

300  =  5k

Divide all sides by 5. 

60  =  ok

Substitute ok = 60 in (1). 

y  =  60x

3. Reply :

Equation of direct variation :

y  =  kx —–(1)

Substitute x = 40 and y = 12.

40  =  ok(12)

40  =  12k

Divide all sides by 12.

10/3  =  ok

Substitute ok = 10/3 in (1). 

y  =  (10/3)x

4. Reply :

Equation of direct variation :

y  =  kx —–(1)

Substitute x = 15 and y = 4. 

4  =  ok(15)

4  =  15k

Divide all sides by 15.

4/15  =  ok

Substitute ok = 4/15 in (1). 

y  =  (4/15)x

5. Reply :

Equation of direct variation :

y  =  kx —–(1)

Substitute x = 16 and y = 48. 

48  =  ok(16)

48  =  16k

Divide all sides by 16.

3  =  ok

Substitute ok = 3 in (1).

y  =  3x

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