Question
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. Line W passes through (0,0), (1,1), and (2,2), while line X passes through (0,0), (-1, 3), and (-2, 6).
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 by a factor of 3.
There is a slope change from positive to negative and by a factor of 3.
The slope is changed by a factor of 3.
The slope is changed by a factor of 3.
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 negative to positive and by a factor of 3.
There is a slope change from negative to positive and by a factor of 3.
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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 by a factor of 3.
There is a slope change from positive to negative and by a factor of 3.
The slope is changed by a factor of 3.
The slope is changed by a factor of 3.
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 negative to positive and by a factor of 3.
There is a slope change from negative to positive and by a factor of 3.
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Answers
GPT-4o mini
To analyze the lines you've described:
1. **Line W** passes through (0,0), (1,1), and (2,2). These points indicate that Line W has a slope of 1 (since the change in y is equal to the change in x).
2. **Line X** passes through (0,0), (-1, 3), and (-2, 6). To determine the slope of Line X, we can use two points, say (0,0) and (-1,3):
- The change in y is \(3 - 0 = 3\).
- The change in x is \(-1 - 0 = -1\).
- Therefore, the slope of Line X is \(\frac{3}{-1} = -3\).
Now, let's summarize the slopes:
- The slope of Line W is **1** (positive).
- The slope of Line X is **-3** (negative).
Therefore, there is a change in slope from positive (1) for Line W to negative (-3) for Line X. The magnitude of the slope also changes; Line W has a slope of 1, while Line X has a slope of -3.
So, the correct response is: **There is a slope change from positive to negative and by a factor of 3.**
1. **Line W** passes through (0,0), (1,1), and (2,2). These points indicate that Line W has a slope of 1 (since the change in y is equal to the change in x).
2. **Line X** passes through (0,0), (-1, 3), and (-2, 6). To determine the slope of Line X, we can use two points, say (0,0) and (-1,3):
- The change in y is \(3 - 0 = 3\).
- The change in x is \(-1 - 0 = -1\).
- Therefore, the slope of Line X is \(\frac{3}{-1} = -3\).
Now, let's summarize the slopes:
- The slope of Line W is **1** (positive).
- The slope of Line X is **-3** (negative).
Therefore, there is a change in slope from positive (1) for Line W to negative (-3) for Line X. The magnitude of the slope also changes; Line W has a slope of 1, while Line X has a slope of -3.
So, the correct response is: **There is a slope change from positive to negative and by a factor of 3.**