Final answer:
The slope of a line using ordered pairs is found using the formula m = (Y2 - Y1) / (X2 - X1). In the context of motion, the slope represents speed, with rise being the change in position and run being the change in time. Displacement and distance are also important concepts, with displacement being the straight-line distance from the start to end points and distance being the total path traveled.
Step-by-step explanation:
To find the slope of a line based on provided ordered pairs, you can use the slope formula: m = (Y2 - Y1) / (X2 - X1). This formula represents the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. In the context of a position versus time graph, the slope represents the speed of the trip, with rise being displacement and run being the time elapsed.
If you have the ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5), you would select any two points to find the slope. For example, using the first and third pair, the slope can be calculated as follows:
- Identify the x and y coordinates for each point: Point 1 (x1, y1) = (294.5, 61), Point 3 (x3, y3) = (605.5, 88.5).
- Apply the slope formula: m = (88.5 - 61) / (605.5 - 294.5).
- Simplify to find the slope: m = 27.5 / 311 = 0.0884.
The graph of the return trip would mirror the initial trip, considering the origin as the starting and ending point. In terms of displacement and distance, if a rider ends up 1 km west of the origin, the displacement, Ax = xf - x0, would be -1 km (since east is positive), while the total distance traveled might be greater depending on the path.
In a three-dimensional space, the Cartesian labeling extends to (x, y, z), where you can also calculate the distance using Pythagoras' theorem, p² = x² + y² + z².