Question

How does the graph show the change from line W to line X. the graph shows line W going from points (10, 10) and (-10, -10) and Line X going from points (9, -3) and (-9, 3)

Answer 1

To analyze the change from line W to line X on the graph, we can examine their slopes and intercepts based on the given points.

1. **Line W**:
- Points: \( (10, 10) \) and \( (-10, -10) \)
- Slope (m): The slope \( m \) of a line can be calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-10 - 10}{-10 - 10} = \frac{-20}{-20} = 1
\]
- This means line W has a slope of 1. The y-intercept can also be observed directly from the points since at \( x = 0 \), \( y = 0 \), indicating it crosses the origin.

2. **Line X**:
- Points: \( (9, -3) \) and \( (-9, 3) \)
- Slope (m): The slope for line X is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-3)}{-9 - 9} = \frac{6}{-18} = -\frac{1}{3}
\]
- The slope of line X is \(-\frac{1}{3}\). To find the y-intercept, we can use one of the points to find the linear equation. Using the point \( (9, -3) \) for \( y = mx + b \):
\[
-3 = -\frac{1}{3}(9) + b \implies -3 = -3 + b \implies b = 0
\]
- Thus, like line W, line X also crosses the origin.

**Summary of Changes from Line W to Line X**:
- **Change in Slope**: Line W has a slope of 1 (rising line), while line X has a slope of \(-\frac{1}{3}\) (falling line). This indicates a change from a positive slope (increasing) to a negative slope (decreasing).
- **Direction**: Line W rises as x increases, whereas line X falls as x increases.
- **Orientation**: The lines are aligned in opposite directions in relation to the axes, with line W going upwards and line X going downwards relative to positive x-axis movement.

Overall, the transition from line W to line X represents a significant shift in both direction and slope.