A direct variation can be express as:
[tex]y=kx[/tex]Now, we know that y=2 when x=6; plugging this values in the equation above and solving for k we have:
[tex]\begin{gathered} 2=6k \\ k=\frac{2}{6} \\ k=\frac{1}{3} \end{gathered}[/tex]Hence our variation in this case is:
[tex]y=\frac{1}{3}x[/tex]Now that we have the expression for the direct variation we plug the value x=3/4 to find y:
[tex]\begin{gathered} y=\frac{1}{3}\cdot\frac{3}{4} \\ y=\frac{1}{4} \end{gathered}[/tex]Therefore when x=3/4 the value of y is 1/4.
