Final answer:
To sketch the solutions to the slope field, we need to first understand what a slope field is. We can analyze the given information and the slope field to sketch the solutions passing through the specified points and identify the interval of positive values of x for which the solutions are increasing.
Step-by-step explanation:
To sketch the solutions to the slope field, we need to first understand what a slope field is. A slope field is a graphical representation of the slopes of solutions to a differential equation at different points on a grid. The slope at each point is represented by a short line called a tangent line. We can use the given information to sketch the solutions that pass through the specified points on a sheet of paper.
To determine the interval of positive values of x for which the solutions are increasing, we can analyze the slope field. If the slope field shows a positive slope at each point within a certain interval, then the solutions will be increasing within that interval. We can examine the slopes at different points on the slope field and identify the intervals with positive slopes.
By analyzing the given information and the slope field, we can sketch the solutions passing through the specified points and identify the interval of positive values of x for which the solutions are increasing.