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.

Question

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

(1 point)
Responses

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.

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

The slope is changed by a factor of 3.

Answer 1

To determine how the graph shows the change from Line W to Line X, we need specific details about the slopes of both lines. However, based on the responses you provided, we can break down what each option implies:

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

   • This means Line W has a negative slope, and Line X has a positive slope, with Line X being three times steeper than Line W.

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

   • This indicates Line W has a positive slope and Line X has a negative slope, with Line X being three times steeper than Line W.

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

   • In this case, Line W has a positive slope and Line X has a negative slope, but they are not at different steepness levels; they are simply opposite in sign.

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

   • This suggests that there is a change in steepness between Line W and Line X, but it does not specify the direction (positive or negative).

To choose the correct response, you would need to look at the specific slopes of Line W and Line X on the graph. If you are noticing that one line changes from a positive slope to a negative slope and vice versa, and whether it's by a factor of 3 or not will depend on the exact measurements of the slopes.

Based on the options you've provided, you would select the statement that accurately reflects the slope analysis you observed between Line W and Line X.

Answer 2

line w starts at -10,-10 and ends at 10,10.
line x starts at 3, -9 and ends at-3,9

Answer 3

To analyze the lines, we need to find the slopes of both Line W and Line X based on the points given.

Line W:

• Points: \((-10, -10)\) to \( (10, 10)\)
• Slope Calculation: \[ \text{slope of Line W} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - (-10)}{10 - (-10)} = \frac{20}{20} = 1 \]
• Slope of Line W: 1 (positive)

Line X:

• Points: \((3, -9)\) to \((-3, 9)\)
• Slope Calculation: \[ \text{slope of Line X} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - (-9)}{-3 - 3} = \frac{18}{-6} = -3 \]
• Slope of Line X: -3 (negative)

Summary of Changes:

1. Line W has a positive slope of 1.
2. Line X has a negative slope of -3.

Transition from Line W to Line X:

• There is a slope change from positive to negative.
• The slopes differ in magnitude - the slope of Line X is 3 times the magnitude of Line W’s slope (as \(|-3| = 3 \times |1|\)).

Correct Response:

Based on this information, the correct interpretation of the change from Line W to Line X is:

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