Let's solve the questions step by step.
Question 1
Part A: Evaluate the points (3, 30) and (12, 120)
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Calculate the rise:
- Rise = \( y_2 - y_1 = 120 - 30 = 90 \)
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Calculate the run:
- Run = \( x_2 - x_1 = 12 - 3 = 9 \)
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Calculate the slope:
- Slope = Rise / Run = \( \frac{90}{9} = 10 \)
To summarize:
- The rise from (3, 30) to (12, 120) = 90
- The run from (3, 30) to (12, 120) = 9
- The slope of the line from (3, 30) to (12, 120) = 10
Part B: Evaluate the points (0, 0) and (6, 60)
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Calculate the rise:
- Rise = \( y_2 - y_1 = 60 - 0 = 60 \)
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Calculate the run:
- Run = \( x_2 - x_1 = 6 - 0 = 6 \)
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Calculate the slope:
- Slope = Rise / Run = \( \frac{60}{6} = 10 \)
To summarize:
- The rise from (0, 0) to (6, 60) = 60
- The run from (0, 0) to (6, 60) = 6
- The slope of the line from (0, 0) to (6, 60) = 10
Question 2
Part C: Compare the slopes from Part A and Part B.
- The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120).
So for the comparison:
- The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120).