To find the slope of the runner’s speed in minutes per mile using a graph, you’ll start by identifying two points on the line that represents the runner’s speed. Each point on the graph typically has coordinates in the format (x, y), where x might represent the time and y represents the speed in minutes per mile.
Once you have your two points, use the formula for the slope, which is:
Slope (m) = (y2 – y1) / (x2 – x1)
Here’s how it works:
- Select two distinct points on the graph: Let’s call them Point 1 (x1, y1) and Point 2 (x2, y2).
- Plug the coordinates into the slope formula: Subtract the y-coordinate of Point 1 from the y-coordinate of Point 2 to find the change in speed. Then, subtract the x-coordinate of Point 1 from the x-coordinate of Point 2 to find the change in time.
- Calculate the slope: The resulting value will give you the slope of the line, indicating how quickly the runner’s speed changes with time.
In the context of the runner’s speed, a positive slope indicates that as time increases, the speed (in minutes per mile) is decreasing, which implies the runner is going faster. Conversely, a negative slope would indicate that the runner is slowing down.