Slope+Fields

A slope field resembles the layout of a standard cartesian plane in thet there are an x axis and y axis, but only only some coordinates are plotted. At these coordinates, a tiny line representative of a generic tangent line is drawn for purposes of representing the slope of the tangent line at that point.

Once the derivative is taken, simply plug in x and y to get the data to be used for the slope field.

If the slope of the tangent line is undefined at a coordinate, then a dotted line can be drawn, but it is more accurate to simply leave out the line because graders can confuse the line as bold.

If the curve is a function then the data on the slope field will be similar vertically.

Example: what slope would the line at (1,2) have if dy/dx=2y-3x?

Answer: plug in to get 4-3=1