Question

Consider the differential equation: dy/dx = x - y at the point (-0.5, 1). Find the direction of the slope at the point (1.5, -1).

Answer 1

The direction of the slope at point (1.5, -1) is positive.

Step-by-step explanation:

To find the direction of the slope at the point (1.5, -1), we can analyze the differential equation and determine the behavior of the slope. The given differential equation is dy/dx = x - y. At the point (-0.5, 1), the value of x is smaller than y, which indicates that the slope is positive. Therefore, the slope at the point (1.5, -1) is also positive.