Identifying Variable Relationships - Algebra II
Card 0 of 28
varies directly with the square root of
. If
, then
. What is the value of
if
?
varies directly with the square root of
. If
, then
. What is the value of
if
?
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
.
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
.
Compare your answer with the correct one above
If
varies directly with
and when
,
due to the effect of a constant, what is the value of
when
?
If varies directly with
and when
,
due to the effect of a constant, what is the value of
when
?
Since
varies directly with
,
where
is a constant.
1. Solve for
when
and
.



2. Use your equation to solve for
when
.


Since varies directly with
,
where
is a constant.
1. Solve for when
and
.
2. Use your equation to solve for when
.
Compare your answer with the correct one above
If
varies indirectly with
and when
,
due to the effect of a constant, what is the value of
when
?
If varies indirectly with
and when
,
due to the effect of a constant, what is the value of
when
?
Since
varies indirectly with
, 
1. Solve for
when
and
.




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


Since varies indirectly with
,
1. Solve for when
and
.
2. Use the equation you found to solve for when
.
Compare your answer with the correct one above
varies directly with
. If
, what is
if
?
varies directly with
. If
, what is
if
?
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:



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:
Compare your answer with the correct one above
varies inversely with
. If
, then what is
equal to when
?
varies inversely with
. If
, then what is
equal to when
?
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:



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:
Compare your answer with the correct one above
varies directly with
and when
. What is
when
?
varies directly with
and when
. What is
when
?
1. Since
varies directly with
:
![y=K\sqrt[3]{x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307727/gif.latex)
2. Use the values given for x and y to solve for K:
![y=K\sqrt[3]{x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307728/gif.latex)
![3=K\sqrt[3]{8}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307729/gif.latex)


3. Use your new equation with the K you solved for to solve for y when x=27:
![y=(\frac{3}{2})\sqrt[3]{27}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307732/gif.latex)

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:
Compare your answer with the correct one above
varies inversely with
. When
. What is the value of
when
?
varies inversely with
. When
. What is the value of
when
?
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:



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:
Compare your answer with the correct one above
varies directly with the square root of
. If
, then
. What is the value of
if
?
varies directly with the square root of
. If
, then
. What is the value of
if
?
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
.
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
.
Compare your answer with the correct one above
If
varies directly with
and when
,
due to the effect of a constant, what is the value of
when
?
If varies directly with
and when
,
due to the effect of a constant, what is the value of
when
?
Since
varies directly with
,
where
is a constant.
1. Solve for
when
and
.



2. Use your equation to solve for
when
.


Since varies directly with
,
where
is a constant.
1. Solve for when
and
.
2. Use your equation to solve for when
.
Compare your answer with the correct one above
If
varies indirectly with
and when
,
due to the effect of a constant, what is the value of
when
?
If varies indirectly with
and when
,
due to the effect of a constant, what is the value of
when
?
Since
varies indirectly with
, 
1. Solve for
when
and
.




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


Since varies indirectly with
,
1. Solve for when
and
.
2. Use the equation you found to solve for when
.
Compare your answer with the correct one above
varies directly with
. If
, what is
if
?
varies directly with
. If
, what is
if
?
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:



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:
Compare your answer with the correct one above
varies inversely with
. If
, then what is
equal to when
?
varies inversely with
. If
, then what is
equal to when
?
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:



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:
Compare your answer with the correct one above
varies directly with
and when
. What is
when
?
varies directly with
and when
. What is
when
?
1. Since
varies directly with
:
![y=K\sqrt[3]{x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307727/gif.latex)
2. Use the values given for x and y to solve for K:
![y=K\sqrt[3]{x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307728/gif.latex)
![3=K\sqrt[3]{8}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307729/gif.latex)


3. Use your new equation with the K you solved for to solve for y when x=27:
![y=(\frac{3}{2})\sqrt[3]{27}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307732/gif.latex)

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:
Compare your answer with the correct one above
varies inversely with
. When
. What is the value of
when
?
varies inversely with
. When
. What is the value of
when
?
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:



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:
Compare your answer with the correct one above
varies directly with the square root of
. If
, then
. What is the value of
if
?
varies directly with the square root of
. If
, then
. What is the value of
if
?
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
.
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
.
Compare your answer with the correct one above
If
varies directly with
and when
,
due to the effect of a constant, what is the value of
when
?
If varies directly with
and when
,
due to the effect of a constant, what is the value of
when
?
Since
varies directly with
,
where
is a constant.
1. Solve for
when
and
.



2. Use your equation to solve for
when
.


Since varies directly with
,
where
is a constant.
1. Solve for when
and
.
2. Use your equation to solve for when
.
Compare your answer with the correct one above
If
varies indirectly with
and when
,
due to the effect of a constant, what is the value of
when
?
If varies indirectly with
and when
,
due to the effect of a constant, what is the value of
when
?
Since
varies indirectly with
, 
1. Solve for
when
and
.




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


Since varies indirectly with
,
1. Solve for when
and
.
2. Use the equation you found to solve for when
.
Compare your answer with the correct one above
varies directly with
. If
, what is
if
?
varies directly with
. If
, what is
if
?
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:



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:
Compare your answer with the correct one above
varies inversely with
. If
, then what is
equal to when
?
varies inversely with
. If
, then what is
equal to when
?
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:



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:
Compare your answer with the correct one above
varies directly with
and when
. What is
when
?
varies directly with
and when
. What is
when
?
1. Since
varies directly with
:
![y=K\sqrt[3]{x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307727/gif.latex)
2. Use the values given for x and y to solve for K:
![y=K\sqrt[3]{x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307728/gif.latex)
![3=K\sqrt[3]{8}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307729/gif.latex)


3. Use your new equation with the K you solved for to solve for y when x=27:
![y=(\frac{3}{2})\sqrt[3]{27}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/307732/gif.latex)

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:
Compare your answer with the correct one above