To determine how the graph shows the change from Line W to Line X, we need to focus on the direction of the slopes and whether or not there is a factor change involved.
If the slope of Line W is positive and the slope of Line X is negative, then the transition shows a change from positive to negative, which is what the first option indicates. Additionally, if the change is by a factor of 3, it would mean Line X's slope is 3 times steeper (or shallower in the case of switching sign) than Line W's slope.
Let's analyze the options:
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"There is a slope change from positive to negative and by a factor of 3." - This would be true if Line W had a positive slope and Line X had a negative slope that was three times greater in magnitude.
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"The slope is changed by a factor of 3." - This is vague as it doesn't specify the direction of the slope change (positive or negative).
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"There is a slope change from negative to positive and by a factor of 3." - This would be true if Line W had a negative slope and Line X had a positive slope that was three times greater in magnitude.
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"There is a slope change from positive to negative and no factor change." - This indicates a change of direction but not a change in steepness.
To choose an option, we need to know whether the slopes are changing from positive to negative and if there is a factor change involved.
If the graph shows Line W with a positive slope and Line X with a negative slope that is three times as steep, the correct answer would be:
There is a slope change from positive to negative and by a factor of 3.