Slope field multiple choice: Which graphic shows dy/dx = x - ky for k > 0?

[tpupble]

Why is it that option C is correct but not A. C is A reflected across the y axis. A would be valid if the value of k is such that the magnitude of ky is less than x. Hence in quadrant 1 and 2, there are mostly positive slopes, and in quadrant 3 and 4, there are mostly negative slopes. C is also valid but if the value of ky is such that the magnitude is more than x, resulting in mostly negative slopes in Q1,2 and mostly positive in Q3,4.

 

[Dr.Peterson]

View attachment 36466
Why is it that option C is correct but not A. C is A reflected across the y axis. A would be valid if the value of k is such that the magnitude of ky is less than x. Hence in quadrant 1 and 2, there are mostly positive slopes, and in quadrant 3 and 4, there are mostly negative slopes. C is also valid but if the value of ky is such that the magnitude is more than x, resulting in mostly negative slopes in Q1,2 and mostly positive in Q3,4.

They tell you that k is positive; so the slope (x - ky) should be negative for positive y along the y axis (and decreasing as y increases). Is that true of A?

Your statement, "A would be valid if the value of k is such that the magnitude of ky is less than x" is meaningless; x and y vary, so this can't describe the entire slope field, only specific points.

 

[blamocur]

View attachment 36466
Why is it that option C is correct but not A. C is A reflected across the y axis. A would be valid if the value of k is such that the magnitude of ky is less than x. Hence in quadrant 1 and 2, there are mostly positive slopes, and in quadrant 3 and 4, there are mostly negative slopes. C is also valid but if the value of ky is such that the magnitude is more than x, resulting in mostly negative slopes in Q1,2 and mostly positive in Q3,4.

Where would you expect to see zero (a.k.a. horizontal) slopes?