For the data in the table, write an equation for the direct variation.

The equation of direct variation is,
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}[/tex]Substitute the values of y and x.
[tex]\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}[/tex]So, the obtained equation will be y=1.35(x).
Let's check with the values of x.
1) If x=4
[tex]\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}[/tex]2) If x=2
[tex]\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}[/tex]3) If x=-2