...forms triangle of area 27 wit positive coordinate axes.
book has answer -3/2 or -3/8
i found first answeer but not second???
let $\displaystyle x_i$ and $\displaystyle y_i$ represent the positive x and y intercepts of the line
$\displaystyle \frac{x_i \cdot y_i}{2} = 27 \implies x_i \cdot y_i = 54$
slope of the line is $\displaystyle m = -\frac{y_i}{x_i}$
$\displaystyle y = mx + b$
$\displaystyle 3 = -\frac{y_i}{x_i} \cdot 4 + y_i$
$\displaystyle 3 = -y_i\left(\frac{4}{x_i} -1\right)$
$\displaystyle 3 = -\frac{54}{x_i} \left(\frac{4}{x_i} -1\right)$
$\displaystyle 3 = -\frac{216}{x_i^2} + \frac{54}{x_i}$
$\displaystyle 3x_i^2 = -216 + 54x_i$
$\displaystyle 3x_i^2 - 54x_i + 216 = 0$
$\displaystyle x_i^2 - 18x_i + 72 = 0$
$\displaystyle (x_i - 6)(x_i - 12) = 0$
$\displaystyle x_i = 6 \implies y_i = 9$ ... $\displaystyle m = -\frac{9}{6} = -\frac{3}{2}$
$\displaystyle x_i = 12 \implies y_i = 4.5$ ... $\displaystyle m = -\frac{4.5}{12} = -\frac{9}{24} = -\frac{3}{8}$
also, in future please post entire problem within the post ... not part in the title, rest in the post. thanks.