Given the graph of the Direct Variation, you can identify this point:
[tex]\mleft(2,4\mright)[/tex]
By definition, the equation of a Direct Variation has this form:
[tex]y=kx[/tex]
Where "k" is the Constant of Variation.
In this case, knowing the point shown before, you can set up that:
[tex]\begin{gathered} x=2 \\ y=4 \end{gathered}[/tex]
Now you can substitute these values into the equation and solve for "k":
[tex]\begin{gathered} 4=k(2) \\ \\ \frac{4}{2}=k \\ \\ k=2 \end{gathered}[/tex]
Therefore, the equation that represents the line given in the exercise is:
[tex]y=2x[/tex]
Since you need to find the value of "y" when:
[tex]x=-15[/tex]
You need to substitute that x-value into the equation and evaluate:
[tex]\begin{gathered} y=2(-15) \\ y=-30 \end{gathered}[/tex]
Hence, the answer is: Option A.
