The form of the direct variation is
[tex]y=kx[/tex]
Where k is the constant of variation
Since the given figure is a parabola that represents a quadratic equation, then
The equation should be
[tex]y=kx^2[/tex]
Let us use the points on the graph to check if all values of k will be equal
If they are equal, then it is a direct variation,
if they are not equal, then it is not a direct variation
Let us use points (2, 2), (4, 8), and (-3, 4.5)
[tex]\begin{gathered} x=2,y=2 \\ 2=k(2)^2 \\ 2=4k \\ \frac{2}{4}=\frac{4k}{4} \\ \frac{1}{2}=k \end{gathered}[/tex][tex]\begin{gathered} x=4,y=8 \\ 8=k(4)^2 \\ 8=16k \\ \frac{8}{16}=\frac{16k}{16} \\ \frac{1}{2}=k \end{gathered}[/tex]
[tex]\begin{gathered} x=-3,y=4.5 \\ 4.5=k(-3)^2 \\ 4.5=9k \\ \frac{4.5}{9}=\frac{9k}{9} \\ \frac{1}{2}=k \end{gathered}[/tex]
Since the values of k are equal, then it is a direct variation
Yes, it is a direct variation
