Question

If y varies inversely as x and y=7 when x=−4, find y when x=2.

Equation: ________

Solution: y = _____________

Answer 1

Step-by-step explanation:

The statement is expressed as

y

∝

1

x

inverse means

1

variable

To convert to an equation introduce k, the constant of variation.

y

=

k

×

1

x

⇒

y

=

k

x

To find k use the given condition that y = 8 when x = 4

8

=

k

4

⇒

k

=

4

×

8

=

32

⇒

equation is

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

y

=

32

x

2

2

∣

∣

∣

−−−−−−−−−−−−

x

=

16

→

y

=

32

16

⇒

y

=

2

when

x

=

16