Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 23
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Question 23 

Which of the following is the slope field for the differential equation ? Select all that apply. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Try finding the coordinates of the points where . Then think about the points where . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. According to the differential equation, if and only if , which occurs precisely along the line . This rules out slope fields (i) and (iii), which do not have horizontal slopes along the line in the fourth quadrant. To choose between slope fields (ii) and (iv), note that the slopes should be positive at the points for which . These are the points that lie above the line . We see that slope field (iv) has lines of negative slope above the line in the fourth quadrant. Thus, the only possible slope field for the differential equation is (ii). 