An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.
First, solve for kk, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
yy
==
88
xx
==
-4−4
yy
==
kxkx
Inverse Variation Formula
88
==
k−4k−4
Substitute known values
88×-4×−4
==
k-4k−4×-4×−4
Multiply -4−4 to both sides
-32−32
==
kk
kk
==
-32−32
Next, rewrite the Inverse Variation Formula with kk substituted.
yy
==
kxkx
yy
==
-32x−32x
Substitute kk
Finally, use the new formula and substitute x=6x=6
yy
==
-32x−32x
New formula
yy
==
-326−326
Substitute x=6x=6
yy
==
-513−513
(i)(i) Equation: y=-32xy=−32x
(ii)(ii) Missing value: y=-513y=−513
Question 2 of 4
2. Question
Given the following, find the equation for the inverse variation and then solve for the missing xx value
An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.
First, solve for kk, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
yy
==
9.59.5
xx
==
-1−1
yy
==
kxkx
Inverse Variation Formula
9.59.5
==
k−1k−1
Substitute known values
9.59.5×-1×−1
==
k-1k−1×-1×−1
Multiply -1−1 to both sides
-9.5−9.5
==
kk
kk
==
-9.5−9.5
Next, rewrite the Inverse Variation Formula with kk substituted.
yy
==
kxkx
yy
==
-9.5x−9.5x
Substitute kk
Finally, use the new formula and substitute y=-0.5y=−0.5
yy
==
-9.5x−9.5x
New formula
-0.5−0.5
==
-9.5x−9.5x
Substitute y=-0.5y=−0.5
-0.5−0.5×x×x
==
-9.5x−9.5x×x×x
Multiply xx to both sides
-0.5x−0.5x
==
(-9.5)(−9.5)
-0.5x−0.5x÷-0.5÷−0.5
==
(-9.5)(−9.5)÷-0.5÷−0.5
Divide both sides by 0.50.5
xx
==
1919
(i)(i) Equation: y=-9.5xy=−9.5x
(ii)(ii) Missing value: x=19x=19
Question 3 of 4
3. Question
Given the following, find the equation for the inverse variation and then solve for the missing xx value
An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.
First, solve for kk, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
yy
==
6.86.8
xx
==
4.24.2
yy
==
kxkx
Inverse Variation Formula
6.86.8
==
k4.2k4.2
Substitute known values
6.86.8×4.2×4.2
==
k4.2k4.2×4.2×4.2
Multiply 4.24.2 to both sides
28.5628.56
==
kk
kk
==
28.5628.56
Next, rewrite the Inverse Variation Formula with kk substituted.
yy
==
kxkx
yy
==
28.56x28.56x
Substitute kk
Finally, use the new formula and substitute y=3y=3
yy
==
28.56x28.56x
New formula
33
==
28.56x28.56x
Substitute y=3y=3
33×x×x
==
28.56x28.56x×x×x
Multiply xx to both sides
3x3x
==
28.5628.56
3x3x÷3÷3
==
28.5628.56÷3÷3
Divide both sides by 33
xx
==
9.529.52
(i)(i) Equation: y=28.56xy=28.56x
(ii)(ii) Missing value: x=9.52x=9.52
Question 4 of 4
4. Question
Given the following, find the equation for the inverse variation and then solve for the missing yy value
An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.
First, solve for kk, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
yy
==
1111
xx
==
77
yy
==
kxkx
Inverse Variation Formula
1111
==
k7k7
Substitute known values
1111×7×7
==
k7k7×7×7
Multiply 77 to both sides
7777
==
kk
kk
==
7777
Next, rewrite the Inverse Variation Formula with kk substituted.
yy
==
kxkx
yy
==
77x77x
Substitute kk
Finally, use the new formula and substitute x=3x=3