Triangle Formed By Axes

Hence, 3x + 4y + 24 = 0 and 3x + 4y - 24 = 0 are equation of straight line

$tan ɸ = slope = \frac{-3}{4}$ , since the slope is negative the line is inclined downwards to the right. We know that $tan ɸ$ is equal to $\frac{opposite side}{adjacent side}$ . We can disregard the negative sign of the slope.

$tan ɸ=$ $\frac{y}{x}=$ $\frac{3}{4}$ . We see that $x=$ $\frac{4}{3}y$

$A=$ $\frac{1}{2}xy$

$24=$ $\frac{1}{2}$ $\frac{4}{3}y(y)$

From here,

$y^2=36$

$y=6$ , we consider only the positive value.

Solving for x, we have

$x=$ $\frac{4}{3}(6)=8$

So the intercepts are $(0,6)$ and $(8,0)$ .

From point-slope form of an equation of a line, we have

$y-y_1=m(x-x_1)$

$y-0=$ $\frac{-3}{4}(x-8)$

$4y=-3x+24$

$3x+4y-24=0$