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Rachel drew the two graphs below.

Graph R

On a coordinate plane, a line goes through points (0, 0) and (2, 1).
Graph S

On a coordinate plane, a line goes through points (0, 0) and (1, 2).

Rachel says that Graph R has a greater constant of variation than Graph S. Which statement explains whether Rachel is correct?
Rachel is correct; Graph S is nonproportional.
Rachel is correct; Graph R goes farther along the x-axis.
Rachel is not correct; both graphs go through the origin and have the same constant of variation.
Rachel is not correct; Graph S is steeper than Graph R.

1 answer

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:

  1. Rachel is correct; Graph S is nonproportional. (Incorrect; both graphs are proportional since they go through the origin.)
  2. 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.)
  3. 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.)
  4. 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.