Generating a slope field is a simple way to think about the solution to a first order differential equation. Consider the differential equation

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Given a point *(x,y),* the function *f* gives the slope, *m, *of the differential equation. If you do this for a set of points , and draw a short line at each point to represent the slope, you can generate a slope field. By choosing a starting point and constructing a line whose slope is *m* at each point, you can construct a solution curve.