The problem asks which of the following can be represented by the equation $y = 2x$, with the choices being Table A, Graph B, both, or neither.

Analyzing the options:

1. Table A:

   • The equation given is $y = 2x$, so for each $x$ value in the table, $y$ should be twice the $x$ value.
   • Checking Table A:
     • When $x = 2$, $y$ is 3. According to $y = 2x$, $y$ should be $2(2) = 4$, not 3.
     • When $x = 4$, $y$ is 6. According to $y = 2x$, $y$ should be $2(4) = 8$, not 6.
     • When $x = 6$, $y$ is 9. According to $y = 2x$, $y$ should be $2(6) = 12$, not 9.
   • Therefore, Table A does not represent the equation $y = 2x$.

2. Graph B:

   • The equation $y = 2x$ represents a straight line with a slope of 2 and a y-intercept of 0.
   • Checking Graph B:
     • The line passes through the origin (0, 0), which fits the equation $y = 2x$.
     • The slope (rise over run) between points on the line matches a slope of 2. For example, from (0,0) to (1,2), the rise is 2 and the run is 1, which gives a slope of 2.
   • Therefore, Graph B represents the equation $y = 2x$.

Conclusion:

The correct answer is B: Graph B only.

Do you want any further details or have any other questions?

Here are some related questions to explore:

1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How can you identify the slope and y-intercept from a graph?
4. Can a table of values always represent a linear equation?
5. What does it mean when a table does not follow a linear relationship?

Tip: When analyzing tables for linear equations, always check if the changes in $y$ correspond consistently with the changes in $x$.