The equation expressing the statement "y varies directly as x" is [tex]y=kx.[/tex]
Explanation
The statement that [tex]y[/tex] varies directly as [tex]x[/tex] is analogous to saying that the ratio of [tex]y[/tex] to [tex]x[/tex] is constant. In other words, when [tex]x[/tex] increases, [tex]y[/tex] likewise increases and that when [tex]x[/tex] decreases, [tex]y[/tex] decreases proportionally.
Mathematically, we express the relationship that the ration of [tex]y[/tex] is to [tex]x[/tex] is constant is expressed as; [tex]\frac{y}{x} =k[/tex] where [tex]k[/tex] is the constant of proportionality.
We can then solve the relationship for [tex]y[/tex] to determine the correct form of the relationship as shown below,
[tex]\frac{y}{x} =k\\\rightarrow y=kx[/tex]
