A graph has a slant asymptote when one degree on the top has one bigger degree than on the bottom. To find the equation I would use synthetic division with numerator divided by denominator. The remainder however is not included because it is not needed. I but the answer into slope point form and start dotting out the graph using the Point slope equation that I got, and the denominator. I can find the y and x intercepts and make key points, which I can get using the graphing calculator.
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