MHB 9.2.2 AP Calculus Exam -- slope field for which DE

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The discussion centers on solving a differential equation (DE) using slope fields, suggesting that observation can lead to the solution. Participants note that while some may prefer to separate variables and integrate, the problem can be approached visually by analyzing the slope field. The slopes near the line are close to -1, indicating a linear relationship. The equation derived is y = -x - 1, leading to the conclusion that the solution resembles option C. The conversation raises questions about confirming the linearity of the solution.
karush
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ok probably if one did a lot of these this could be solved by observation
others separate the variables and take to Integral to get the equation
 

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karush said:
ok probably if one did a lot of these this could be solved by observation
others separate the variables and take to Integral to get the equation

meant to be done by observation ... note the slopes near this line are close to a value of -1

the equation of the line is about $\color{red}y = -x-1 \implies y+x=-1$

what do you think?
 

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that looks like C

but how would you it was a line?
 

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