Final answer:
To match a slope field with its differential equation, one must analyze how slopes change across the field in response to changes in x and y. Without the actual slope field image, it's not possible to accurately identify the corresponding differential equation. However, it can be said that given linear equations, A and C are straightforward linear, and B is also linear due to the linearity of its terms.
Step-by-step explanation:
The student is asking about slope field representations of differential equations. To determine which differential equation corresponds to a given slope field, we analyze the way the slopes change across the field. A slope field for dx/dy = yx would show that as the values of x and y increase, the slopes of the lines would also increase proportionally since the slope at each point (x, y) is just the product of x and y. For dx/dy = -yx, the slopes would be the negative of that situation, meaning that as x and y become more positive, the slopes would become more negative. For dx/dy = yx², the dependence on x is stronger, as the slope would square the x value and then multiply by y, leading to more dramatic changes in slope as x changes. Similarly, dx/dy = -yx² would show the same pattern but with negative slopes. Lastly, for dx/dy = y²x, the slopes would depend on the square of y, altering the dynamic further.
Correct identification requires a visualization of the slope field, which is not provided in this context. Without the graphic, the responses to the representations of differential equations cannot be specified accurately. However, generally speaking, linear equations like A and C (A: y = -3x, C: y = -9.4 - 2x) are indeed linear, and Equation B (B: y = 0.2 + 0.74x) is also linear despite the presence of a constant term.