Angular Coeficient of a Line Passing Through (4,3) in 1st Quadrant with Area 27

[amarante]

Homework Statement

What is the angular coeficient of a straight line that passes through (4,3), if it satifies x>0 and y>0, and it is one of the sides of a triangle with total area of 27 (units of area).

calcule o coeficiente angular de um reta que passe por (4,3) de modo que a parte da reta no primeiro quadrante forma um triângulo de área 27 com os eixos coordenados positivos.

Homework Equations

I know that the area of a triangle is area = base * height/2 . I know the equation of the straigh line is y = aX + B, where "a" is what I am looking for. But I am stucked! I can't find a nice relation.

The Attempt at a Solution

I've tried to use the relation Area = 1/2 * D
Where D is the determinant of a matrix with the 3 vertices of the triangle, with an aditional columns of "1". But, couldn't go any further... any ideas?

 

[LCKurtz]

Homework Statement

What is the angular coeficient of a straight line that passes through (4,3), if it satifies x>0 and y>0, and it is one of the sides of a triangle with total area of 27 (units of area).

calcule o coeficiente angular de um reta que passe por (4,3) de modo que a parte da reta no primeiro quadrante forma um triângulo de área 27 com os eixos coordenados positivos.

Homework Equations

I know that the area of a triangle is area = base * height/2 . I know the equation of the straigh line is y = aX + B, where "a" is what I am looking for. But I am stucked! I can't find a nice relation.

The Attempt at a Solution

I've tried to use the relation Area = 1/2 * D
Where D is the determinant of a matrix with the 3 vertices of the triangle, with an aditional columns of "1". But, couldn't go any further... any ideas?

I assume the axes form the other two sides of the triangle. Write the equation of the line though $(4,3)$ with slope $a$. Its $x$ and $y$ intercepts will give you the base and height in terms of $a$. Then set the area, now in terms of $a$, equal to 27 and solve for $a$.

 

[amarante]

Perfect! I got it. Thank you so much!

I got a solution with two possibilities, a= -1.5, or a = -0.375.

Thanks!