Option A: Direct variation ; [tex]k=-2[/tex]
Explanation:
From the graph, some of the points that the line passes through are [tex](1,-2)[/tex], [tex](-1,2)[/tex] and [tex](-2,4)[/tex]
Thus, direct variation is the relationship between two variable in which one is the constant multiple of the other.
The expression can be written as [tex]\frac{y}{x} =k[/tex]
Substituting the coordinate [tex](1,-2)[/tex] in [tex]\frac{y}{x} =k[/tex], we get,
[tex]\frac{-2}{1} =k\\-2=k[/tex]
Also, substituting the coordinate [tex](-1,2)[/tex], we get
[tex]\frac{2}{-1} =k\\-2=k[/tex]
Thus, [tex]k=-2[/tex] which is direct variation.
Hence, Option A is the correct answer.
