To determine if the point (6, 1850) is on the line that represents the instructor's financial situation, we first need to derive the equation of that line.
Let's break it down:
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Understanding the situation:
- The instructor has $3,500 saved.
- He spends $275 monthly on rent.
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Plane context:
- We can define the x-axis as the number of months (x), and the y-axis as the amount of money remaining (y) after paying the rent.
- The initial amount saved is $3,500, which means at month 0 (x = 0), y = 3500.
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Setting up the equation:
- After 1 month, the amount left would be: \[ y = 3500 - 275x \]
- This equation describes how the remaining funds decrease over time due to rent payments.
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Checking if the point (6, 1850) is on the line:
- Plug x = 6 into the equation to see if we get y = 1850: \[ y = 3500 - 275 \cdot 6 \]
- Calculate: \[ y = 3500 - 1650 = 1850 \]
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Conclusion:
- Since substituting x = 6 into the equation gives us y = 1850, the point (6, 1850) is indeed on the line represented by the equation \( y = 3500 - 275x \).
Thus, the instructor is correct; the point (6, 1850) is on the line that describes his financial situation according to the equation derived.