Answer:
constant of variation(k) is, 250.
[tex]y = \frac{250}{x}[/tex]
Step-by-step explanation:
The inverse variation says that:
[tex]y \propto \frac{1}{x}[/tex]
then, the equation is in the form of :
[tex]y = \frac{k}{x}[/tex] ....[1] where, k is the constant of variation
As per the statement:
Suppose that y varies inversely with x.
then,
by definition of inverse variation we have;
[tex]y = \frac{k}{x}[/tex]
When x = 2.5 and y = 100 then
Substitute these in [1] we have;
[tex]100 = \frac{k}{2.5}[/tex]
Multiply 2.5 both sides we have;
[tex]250 = k[/tex]
or
k = 250
⇒[tex]y = \frac{250}{x}[/tex]
Therefore, the constant of variation is, 250 and the equation we get [tex]y = \frac{250}{x}[/tex]
