To analyze Jason's graph, we can determine a few key pieces of information:
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Unit Rate: Since the graph is linear and starts from the origin, the slope of the line will give us the unit rate (the rate at which Jason completes puzzles per hour). The coordinates of two points on the line can help us calculate this.
If we take the point (3, 1) which means after 3 hours, Jason has completed 1 puzzle.
Let's denote (x₁, y₁) = (3, 1) and the origin (0,0) = (x₀, y₀).
We can calculate the slope (m), which is the change in y divided by the change in x:
\[ m = \frac{y₁ - y₀}{x₁ - x₀} = \frac{1 - 0}{3 - 0} = \frac{1}{3} \]
This means that Jason completes \( \frac{1}{3} \) of a puzzle per hour.
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Puzzles Completed in a Given Time: From the slope \( \frac{1}{3} \) (puzzles/hour), we can then figure out how many puzzles Jason completes in any given amount of time.
For example, if he works on puzzles for 5 hours, we can calculate the number of puzzles completed as follows:
\[ \text{Puzzles completed} = \text{hours worked} \times \text{unit rate} = 5 \times \frac{1}{3} = \frac{5}{3} \approx 1.67 \text{ puzzles (or 1 full puzzle and some portion of a second one)} \]
Based on this analysis, we can conclude:
- Jason’s unit rate is: \( \frac{1}{3} \) puzzles per hour.
- Jason completes 5 puzzles in about: 15 hours (since \(5 \div \frac{1}{3} = 15\)).
Therefore, the answers to your blanks are:
- Jason’s unit rate is \( \frac{1}{3} \) puzzles per hour.
- Jason completes 5 puzzles in about 15 hours.
2 answers