Option A : yes; [tex]-\frac{2}{3}[/tex]
Explanation:
The table represents a proportional relationship because the x-values increases at a constant rate of 3 units and y-values increases at a constant rate of 2 units.
Since, the table represents a proportional relationship, the constant ratio is given by [tex]\frac{y}{x}[/tex]
From the table, let us substitute the values for x and y
For [tex]x=3[/tex] and [tex]y=-2[/tex], the constant ratio is
[tex]\frac{y}{x}=\frac{-2}{3}[/tex]
Similarly, for [tex]x=6[/tex] and [tex]y=-4[/tex], the constant ratio is
[tex]\frac{y}{x}=\frac{-4}{6} =\frac{-2}{3}[/tex]
For [tex]x=9[/tex] and [tex]y=-6[/tex], the constant ratio is
[tex]\frac{y}{x}=\frac{-6}{9} =\frac{-2}{3}[/tex]
For [tex]x=12[/tex] and [tex]y=-8[/tex], the constant ratio is
[tex]\frac{y}{x}=\frac{-8}{12} =\frac{-2}{3}[/tex]
Thus, the constant ratio is [tex]-\frac{2}{3}[/tex]
