Respuesta :

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.

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