To determine whether Rachel is correct about the slopes of Graph R and Graph S, we need to analyze the graphs. Without seeing the graphs, I can't definitively conclude about their slopes. However, I can guide you through the options provided:
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Rachel is correct; Graph R goes farther along the x-axis. - This statement alone does not determine the slope of the graphs. The slope is defined as the rise over run (the change in y over the change in x), not how far the graph extends along the x-axis.
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Rachel is not correct; both graphs go through the origin and have the same slope. - If both graphs do go through the origin and have the same slope, Rachel would indeed be incorrect.
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Rachel is not correct; Graph S is steeper than Graph R. - If Graph S has a greater slope (is steeper) than Graph R, then Rachel is incorrect.
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Rachel is correct; Graph S is non-proportional. - This could suggest that Graph S has a different type of relationship that may not yield a constant slope, but it doesn't inherently validate Rachel's claim about the slopes being greater in Graph R.
Based on the definition of slope and the context, if Graph R is indeed less steep than Graph S, then the correct response would be:
Rachel is not correct; Graph S is steeper than Graph R.
If, however, the two graphs actually have the same slope or if both go through the origin and show proportionality but are not the same slope, you would mark it differently.
Ultimately, please reference the actual graphs to confirm your answer against the conditions described.