Find the equation of the line of slope -3/4 that forms with the coordinate axes a triangle which has the area of 24 square units.

First the form of the equation would
be;

y= mx + b, where m is the
slop.

==> y = (-3/4)x +
b

when x = 0, then y = (-3/4) 0 + b=
b

then the point where the line intersect with the y-axis
is (0,b)

when y = 0 , then (-3/4) x +b=
0

==> (3/4) x=
b

==> x= (4/3)b

then
the point where the line intersect with the x-axis is  (4b/3,
0)

but, the area of the triangle
is:

A= 1/2 * 4b/3 * b

24 = 1/2
* 4b/3 *b

24 = 1/2 * 4b^2/3 = 4b^2
/6

==> b^2 =
24*6/4

==> b^2 =
36

==> b = 6, -6

then
the eqution of teh slope is:

y = (-3/4) x + 6    and y=
(-3/4)x -6