Answer:

1. if y varies inversely as x then there is constant k such as

y = k/x

hence, for y = -2 , when x = -8, then

-2 = k/-8

k = -8 × (-2)

k = 16

for y = 6 we have

6 = 16/x

6x = 16

6x/6 = 16/6

x = 16/6 ÷ 2/2

x = 8/3

check:

6 = 16/8/3

6 = 16 × 3/8

6 = 48/8

6 = 6 ✔️

2. if m varies inversely as n then there is constant k such as

m = k/n

hence, for m = -8 , when n = 3, then

-8 = k/3

k = 3 × (-8)

k = -24

for n = 12 we have

m = -24/12

m = -24/12 ÷ 12/12

m = -2

check:

-2 = -24/12

-2 = -2 ✔️

3. if y varies inversely as x then there is constant k such as

y = k/x

hence, for y = 10, when x = 5, then

10 = k/5

k = 5 × 10

k = 50

for x = 15 we have

y = 50/15

y = 50/15 ÷ 5/5

y = 10/3

check:

10/3 = 50/15

10/3 = 50/15 ÷ 5/5

10/3 = 10/3 ✔️