Question 1042983
<pre><b><font size=4>Since the slope is -1, we substitute -1 in the
slope intercept form

y = mx + b 

and get

y = -1x + b

or

y = -x + b


The y coordinate is (0,b).

We find the x-intercept by substituting y=0 and solving
for x:

0 = -x + b

x = b

So the x-intercept is (b,0)

We graph a typical such line:

{{{drawing(200,200,-6,6,-6,6,line(-13,17,13,-9),
locate(0,0,"(0,0)"),
red(line(-15,0,15,0),line(0,-15,0,15)),
green(triangle(0.02,0.02,3.98,.02,.02,3.98)),
locate(.3,4.7,"(0,b)"), locate(4,1.3,"(b,0)")

 )}}}

We want the area of the green triangle:

The area of a triangle is given by the formula:

{{{Area}}}{{{""=""}}}{{{expr(1/2)base*height}}}

The base is b and the height is also b
We are give that the area = 8, substituting:

{{{8}}}{{{""=""}}}{{{expr(1/2)b*b}}}

{{{8}}}{{{""=""}}}{{{expr(1/2)b^2}}}

Multiply through by 2

{{{16}}}{{{""=""}}}{{{b^2}}}

Take square roots of both sides, remembering ±

{{{"" +- sqrt(16)}}}{{{""=""}}}{{{b}}}

{{{"" +- 4)}}}{{{""=""}}}{{{b}}}

So there are two triangles. One for b=4 and one 
for b=-4, the two green triangles below:
 
{{{drawing(200,200,-6,6,-6,6,line(-13,17,13,-9),
locate(0,0,"(0,0)"),line(-13,9,13,-17),
locate(-4,1.3,"(-4,0)"),

red(line(-15,0,15,0),line(0,-15,0,15)),locate(.3,-3.7,"(0,-4)"),
green(triangle(0.02,0.02,3.98,.02,.02,3.98),triangle(-4,0,0,0,0,-4)),
locate(.3,4.7,"(0,4)"), locate(4,1.3,"(4,0)")

 )}}}

Edwin</pre></font>