# Algebra II : Identifying Variable Relationships

## Example Questions

### Example Question #511 : Algebra Ii

varies directly with the square root of . If , then  . What is the value of  if ?

None of these answers are correct.

Explanation:

If  varies directly with the square root of , then for some constant of variation

If , then ; therefore, the equation becomes

or

.

Divide by 5 to get , making the equation

.

If , then .

### Example Question #1 : Variable Relationships

If  varies directly with  and when  due to the effect of a constant, what is the value of  when ?

Explanation:

Since  varies directly with  where  is a constant.

1. Solve for  when  and .

2. Use your equation to solve for  when .

### Example Question #2 : Variable Relationships

If  varies indirectly with  and when  due to the effect of a constant, what is the value of  when ?

Explanation:

Since  varies indirectly with

1. Solve for  when  and .

2. Use the equation you found to solve for  when .

### Example Question #3 : Variable Relationships

varies directly with . If , what is  if

Explanation:

1. Since  varies directly with

with K being some constant.

2. Solve for K using the x and y values given:

3. Use the equation you solved for to find the value of y:

### Example Question #1 : Identifying Variable Relationships

varies inversely with . If , then what is  equal to when  ?

Explanation:

1. Since  varies indirectly with :

2. Use the given x and y values to determine the value of K:

3. Using the equation along with the value of K, find the value of y when x=5:

### Example Question #2 : Identifying Variable Relationships

varies directly with  and when . What is  when ?

Explanation:

1. Since  varies directly with :

2. Use the values given for x and y to solve for K:

3. Use your new equation with the K you solved for to solve for y when x=27:

### Example Question #6 : Variable Relationships

varies inversely with . When . What is the value of  when ?

Explanation:

1. Since y varies indirectly with :

2. Solve for K using the x and y values given:

3. Using the equation you created by solving for K, find y when x=100: