Let's calculate step by step for each part.
Part A
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Finding the rise from (3, 30) to (12, 120): \[ \text{Rise} = y_2 - y_1 = 120 - 30 = 90 \]
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Finding the run from (3, 30) to (12, 120): \[ \text{Run} = x_2 - x_1 = 12 - 3 = 9 \]
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Finding the slope: \[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{90}{9} = 10 \]
Part B
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Finding the rise from (0, 0) to (6, 60): \[ \text{Rise} = y_2 - y_1 = 60 - 0 = 60 \]
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Finding the run from (0, 0) to (6, 60): \[ \text{Run} = x_2 - x_1 = 6 - 0 = 6 \]
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Finding the slope: \[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{60}{6} = 10 \]
Part C
Now we compare the slopes:
- The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120).
Summary of Answers
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Part A:
- Rise: 90
- Run: 9
- Slope: 10
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Part B:
- Rise: 60
- Run: 6
- Slope: 10
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Part C conclusion: The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120).