Answer:
k is the constant of variation.
Step-by-step explanation:
In direct variation:
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
In inverse variation:
[tex]y\propto \frac{1}{x}[/tex]
[tex]y=\frac{k}{x}[/tex]
[tex]yx=k[/tex]
In both cases k is the constant of variation
The given equation is
[tex]a=\frac{k}{b}[/tex]
We need to find the value of k in this equation.
First we have to isolate k on one side of the equation.
Multiply both sides by b to isolate k on right side.
[tex]a\times b=\frac{k}{b}\times b[/tex]
Cancel out the common factors.
[tex]ab=k[/tex]
Interchange the sides of the equation.
[tex]k=ab[/tex]
It means a and b are inversely proportional.
Therefore, the k is the constant of variation.
