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 k, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
y
=
8
x
=
-4
y
=
kx
Inverse Variation Formula
8
=
k−4
Substitute known values
8×-4
=
k-4×-4
Multiply -4 to both sides
-32
=
k
k
=
-32
Next, rewrite the Inverse Variation Formula with k substituted.
y
=
kx
y
=
-32x
Substitute k
Finally, use the new formula and substitute x=6
y
=
-32x
New formula
y
=
-326
Substitute x=6
y
=
-513
(i) Equation: y=-32x
(ii) Missing value: y=-513
Question 2 of 4
2. Question
Given the following, find the equation for the inverse variation and then solve for the missing x 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 k, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
y
=
9.5
x
=
-1
y
=
kx
Inverse Variation Formula
9.5
=
k−1
Substitute known values
9.5×-1
=
k-1×-1
Multiply -1 to both sides
-9.5
=
k
k
=
-9.5
Next, rewrite the Inverse Variation Formula with k substituted.
y
=
kx
y
=
-9.5x
Substitute k
Finally, use the new formula and substitute y=-0.5
y
=
-9.5x
New formula
-0.5
=
-9.5x
Substitute y=-0.5
-0.5×x
=
-9.5x×x
Multiply x to both sides
-0.5x
=
(-9.5)
-0.5x÷-0.5
=
(-9.5)÷-0.5
Divide both sides by 0.5
x
=
19
(i) Equation: y=-9.5x
(ii) Missing value: x=19
Question 3 of 4
3. Question
Given the following, find the equation for the inverse variation and then solve for the missing x 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 k, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
y
=
6.8
x
=
4.2
y
=
kx
Inverse Variation Formula
6.8
=
k4.2
Substitute known values
6.8×4.2
=
k4.2×4.2
Multiply 4.2 to both sides
28.56
=
k
k
=
28.56
Next, rewrite the Inverse Variation Formula with k substituted.
y
=
kx
y
=
28.56x
Substitute k
Finally, use the new formula and substitute y=3
y
=
28.56x
New formula
3
=
28.56x
Substitute y=3
3×x
=
28.56x×x
Multiply x to both sides
3x
=
28.56
3x÷3
=
28.56÷3
Divide both sides by 3
x
=
9.52
(i) Equation: y=28.56x
(ii) Missing value: x=9.52
Question 4 of 4
4. Question
Given the following, find the equation for the inverse variation and then solve for the missing y 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 k, the constant of variation, by plugging in the known values to the Inverse Variation Formula.
y
=
11
x
=
7
y
=
kx
Inverse Variation Formula
11
=
k7
Substitute known values
11×7
=
k7×7
Multiply 7 to both sides
77
=
k
k
=
77
Next, rewrite the Inverse Variation Formula with k substituted.