Final answer:
The best explanation is option (C) because the graph cannot represent the proportional relationship y = 0.5x correctly if it has a y-intercept of 50, since a proportional relationship's graph should pass through the origin (0,0) and have a slope equal to the proportionality constant.
Step-by-step explanation:
To determine whether the graph correctly represents the proportional relationship y = 0.5x, we need to look at the characteristics of the graph and the equation. For a relationship to be proportional, the graph should be a straight line that passes through the origin, which means the y-intercept should be zero and the slope should represent the constant of proportionality (k). If the equation provided is y = 0.5x, then any graph that accurately represents this would have a slope of 0.5 and a y-intercept of 0. A line with different y-intercept or slope would not represent the equation correctly.
If the line shown has a positive slope and a y-intercept of 50, as stated in the hint, then the graph does not represent the equation y = 0.5x because the y-intercept should be zero, not 50. Statement A and B cannot be correct as they both affirm the graph does represent the equation, which it does not. Statement D is incorrect because proportions can indeed be represented on a graph. Therefore, the best answer is statement (C) "It does not, the points shown would not be part of y = 0.5x" as it correctly identifies that the graph's y-intercept does not match the requirements for the proportional relationship y = 0.5x.