To plot a ray representing the relationship between Paola's total miles and hours, you will need to make some assumptions based on typical relationships, as the exact relationship isn't provided.
If we assume that Paola's mile count increases linearly with hours spent, we can illustrate this by plotting points on a graph.
Steps to Plot the Ray:
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Define the relationship: Let's say for every hour Paola runs, she covers a certain number of miles. We can define a slope, for example, 2 miles per hour. Therefore, if she runs for \( h \) hours, then the total miles \( M \) can be represented as: \[ M = 2h \]
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Choose points: You can start with the origin (0,0) and pick some additional values based on the slope:
- If \( h = 0 \) then \( M = 0 \) → Point (0, 0)
- If \( h = 1 \) then \( M = 2 \) → Point (1, 2)
- If \( h = 2 \) then \( M = 4 \) → Point (2, 4)
- If \( h = 3 \) then \( M = 6 \) → Point (3, 6)
- If \( h = 4 \) then \( M = 8 \) → Point (4, 8)
- If \( h = 5 \) then \( M = 10 \) → Point (5, 10)
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Plot the Ray:
- Start from the origin (0,0).
- Use a ruler or straight edge to create a line extending from (0, 0). The line will go through the plotted points above.
- Extend this ray beyond (5, 10) to represent that it continues indefinitely in that direction.
Graph Configuration:
- Horizontal Axis (Hours): Ranges from -0.4 to 5.4
- Vertical Axis (Total Miles): Ranges from -1.4 to 12.6
The ray starts from the origin (0,0) and goes up to the right, which illustrates that as hours increase, the total miles also increase proportionally according to the linear relationship defined.
Visualization Tip:
If you're using graphing software, you can enter the coordinates defined above and draw a line starting from (0,0) and extending into the first quadrant of the graph.
Note:
If there's a specific slope or relationship you wish to use that differs from the 2 miles per hour example I used, please adjust the points accordingly based on that slope.