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mindauggas
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Homework Statement
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.
Homework Equations
Not given, but I think S(triangle)=ah/2 and point-slope form of the equation of a line will come in handy.
The Attempt at a Solution
I notice that since [itex]S^{(triangle)}=\frac{ah}{2}[/itex] and S=27, ah=54. Because h is the y coordinate and a is the length of the triangle (but not the x coordinate - since the triangle might not pass trough the origin) y=h.
To find x coordinate I mark the x of the point (x,0) (where the line intersects the x axis) - x[itex]_{1}[/itex], and the x at y=h as x[itex]_{2}[/itex]. Now x[itex]_{2}[/itex]=x[itex]_{1}[/itex]+a.
I noticed that y[itex]_{(at:y=h)}[/itex]*a=54
I can also us the point (x[itex]_{1}[/itex],0) and the given point (4,3) to find an expression of the slope [itex]m=\frac{3}{4-x}[/itex].
Stuck here, I do not know how to glue this information together or is it really necessary ... please help.
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