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.
-
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.
-
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.
1 answer