The text asks: Find the possible slopes of a line that passes through (4,3) so that the portion of the line in the first quadrant forms a triangle of area 27 with the positive coordinate axes.

I know that the equation for finding the area of a triangle is $\displaystyle \frac{1}{2}bh$. How do i go about solving this algebraically? The answers in the book are $\displaystyle \frac{-3}{2}, \frac{-3}{8}$. I do not know how they arrived at these answers. I don't know how you could graph it without first determining more than one set of points. Any help would be greatly appreciated. Thanks.