hello
the values given are
[tex]\begin{gathered} x\text{ y} \\ -6\text{ 2} \\ -9\text{ 3} \\ -15\text{ 5} \end{gathered}[/tex]now we can name the values accordingly
[tex]\begin{gathered} x_1=-6 \\ y_1=2_{} \\ x_2=-9 \\ y_2=3 \\ x_3=-15 \\ y_3=5 \end{gathered}[/tex]now let's see how y varies with x
when y1 = 2, x1 = -6
when y increases, x decreases, this is an inverse proportion and hence y does not varies directly with x.
now let's find the constant of proportionality.
note: the value of x increases negatively and y increases
[tex]\begin{gathered} y\propto-\frac{1}{x} \\ y_1=2 \\ x_1=-6 \\ y\propto-\frac{1}{x} \\ y=-\frac{k}{x} \\ -k=yx \\ k=-yx \\ k=-(y_1\times x_1) \\ k=-(2\times6) \\ k=-12 \end{gathered}[/tex]
