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Two lines marked line X and line W are drawn on a coordinate plane. Both axes range from negative 10 to 10 in unit increments.

How does the graph show the change from Line W to Line X ?

(1 point)
Responses

There is a slope change from positive to negative and no factor change.
There is a slope change from positive to negative and no factor change.

There is a slope change from positive to negative and by a factor of 3.
There is a slope change from positive to negative and by a factor of 3.

There is a slope change from negative to positive and by a factor of 3.
There is a slope change from negative to positive and by a factor of 3.

The slope is changed by a factor of 3.
The slope is changed by a factor of 3.

1 answer

To determine how the graph shows the change from Line W to Line X, we need to analyze both the slopes and any factors involved.

  1. Slope Change: If the slope of Line W is positive and the slope of Line X is negative, then there has been a change from positive to negative slope. Similarly, if Line W is negative and Line X is positive, the change is from negative to positive.

  2. Factor Change: A change by a factor of 3 implies that the slope of Line X is either three times steeper than Line W or that Line W’s slope has been decreased to one-third.

Without a visual representation of the lines, the specific situations in the responses become ambiguous. Generally, here’s how we would interpret the responses based on slope changes and factors:

  • If you confirm that the slope indeed goes from positive to negative or vice versa, the corresponding statement will be True.
  • If you can determine the factor increase or decrease specifically (like it being exactly 3), then those statements can be confirmed.

Given the responses provided, one of them must be aligned with the observed changes on the graph.

Here are the key interpretations:

  • If there is a change from positive to negative without any scaling in slope: "There is a slope change from positive to negative and no factor change."
  • If it changes from positive to negative by a factor of 3: "There is a slope change from positive to negative and by a factor of 3."
  • If it changes from negative to positive by a factor of 3: "There is a slope change from negative to positive and by a factor of 3."
  • If it simply states a change by a factor of 3 without context: "The slope is changed by a factor of 3."

If you have specific numeric slopes or angles, please provide them for a more precise conclusion. Otherwise, based on typical linear transformations, choose the response that best matches the observed changes in the slopes from the graph.