To determine whether Rachel is correct regarding the constants of variation for Graph R and Graph S, we first need to understand what the constant of variation means. The constant of variation (or slope) is calculated as the change in y divided by the change in x (rise/run).
For Graph R:
- Points: (0, 0) and (2, 1)
- Slope = (1 - 0) / (2 - 0) = 1 / 2 = 0.5
For Graph S:
- Points: (0, 0) and (1, 2)
- Slope = (2 - 0) / (1 - 0) = 2 / 1 = 2
Now, we compare the slopes (constants of variation):
- Graph R has a slope of 0.5.
- Graph S has a slope of 2.
Since 0.5 < 2, this means that Graph S has a greater constant of variation than Graph R.
Now, let's evaluate the statements:
- Rachel is correct; Graph S is nonproportional. (Incorrect; both graphs are proportional since they go through the origin.)
- Rachel is correct; Graph R goes farther along the x-axis. (Incorrect; while Graph R extends farther along the x-axis, that does not affect the constants of variation.)
- Rachel is not correct; both graphs go through the origin and have the same constant of variation. (Incorrect; they do go through the origin, but they do not have the same constant of variation.)
- Rachel is not correct; Graph S is steeper than Graph R. (Correct; Graph S has a greater slope, which means it is steeper.)
Thus, the correct statement is: Rachel is not correct; Graph S is steeper than Graph R.