Answer:
y = 2x
Step-by-step explanation:
A proportional relationship is one in which two quantities vary directly with each other:
[tex]\boxed{\begin{array}{c}\underline{\textsf{Proportional Relationship}}\\\\\Large\text{$y=kx$}\\\\\textsf{where $k$ is the constant of proportionality}\end{array}}[/tex]
The graph of a proportional relationship passes through the origin (0, 0).
Every table includes the point (-2, -4). Therefore, to graph the line, simply draw a straight line through the points (-2, -4) and (0, 0).
To find the equation of the line, we can substitute (-2, -4) into y = kx and solve for k:
[tex]-4=k(-2)\\\\\\k=\dfrac{-4}{-2}\\\\\\k=2[/tex]
Therefore, the equation of the line that passes through point (-2, -4) and the origin (0, 0) is:
[tex]y=2x[/tex]
To determine which table represents a proportional relationship, we can substitute x = -1, x = 1 and x = 2 into the equation of the line, y = 2x:
[tex]x=-1 \implies y=2(-1)=-2[/tex]
[tex]x=1 \implies y=2(1)=2[/tex]
[tex]x=2 \implies y=2(2)=4[/tex]
Therefore, the 3rd table represents a proportional relationship.
