Hi there!
I think the slope of the line crossing over the graph is negative.
Why?
Because y=<span><span>−<span>0.666667x</span></span>−7.666667 OR, read below!</span>
We will get a negative answer, to show that our slope is negative.
We'll solve for y instead of x.
2x + 3y + 23 = 0
1) Add -23 to both sides. (We're already starting out with a negative!)
<span><span><span><span><span>2x </span>+<span> 3y </span></span>+ 23 </span>+ <span>−23</span></span> =<span> 0 + <span>−23</span></span></span>
<span><span><span>
</span></span></span><span><span><span>2x </span>+ <span>3y </span></span>= <span>−23</span></span>
<span><span>
</span></span>
2) Add -2x to both sides.
<span><span><span><span>2x </span><span><span><span>+ <span>3y</span></span> + <span>−<span>2x </span></span></span>= <span><span>−23 </span>+ <span>−<span>2x</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span /></span></span></span><span><span><span><span>
</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>
</span></span></span></span><span><span>3y </span>= <span><span>−<span>2x </span></span>− 23</span></span></span></span></span>
<span><span><span><span><span>
</span></span></span></span></span>
<span><span><span><span><span /></span></span></span></span>
<span><span><span><span><span>
</span></span>3) Divide both sides by 3.</span></span></span>
<span><span><span>
</span></span></span>
<span><span><span>
</span></span></span>
3y/3 = -2x - 23/3
y = -2/3x + -23/3
So, now that we've done all 3 steps, your answer is
y = -2/3x + -23/3, which is a negative answer!
Now we see that the slope of <span><span><span><span>2x</span>+<span>3y</span></span>+23</span>=0 is negative.</span>
Hope this helps! :D
Meant to add - The /'s are fraction bars
such that the sequence is recursively given by
to find an explicit formula for the 
th term.
