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in this video were going to talk about how to draw a slope field and how to match it with the appropriate equation so lets talk about slopes if we have a slope of 0 what does that mean a slope of zero represents a horizontal line which looks like this now if we have a slope of one we have a line thats going up at a 45 degree angle and if the slope is two its going to go up at a higher angle now if the slope is negative one its going to go down at an angle of 45 degrees and if its negative two even more so now what about if the slope is very large if its a high number then youre going to have a vertical line or if its undefined you still will have a vertical line so these are some things that you want to keep in mind when drawing a slope field so lets start with a practice problem lets say we have the differential equation y prime is equal to x go ahead and draw the slope field that corresponds to this equation so lets make a table were gonna have x y and y prime now y prim