what is the general solution to the differential equation that generated the slope field?

Explanation:

Step1: Analyze the slope - field pattern

By observing the slope - field, we can see that the slope at each point $(x,y)$ is a constant value. The slopes are horizontal and seem to be equal for all $x$ values at a fixed $y$ value. This indicates that $\frac{dy}{dx}=k$, where $k$ is a constant. In this case, by looking at the direction of the line - segments, we can assume $\frac{dy}{dx}=0$.

Step2: Solve the differential equation

The differential equation $\frac{dy}{dx}=0$ can be solved by separating variables. We have $dy = 0\cdot dx$. Integrating both sides: $\int dy=\int0\cdot dx$. The integral of $dy$ is $y$ and the integral of $0\cdot dx$ is a constant $C$. So $y = C$.

Answer:

$y = C$