Quadratic equation in a graph

Question

The question is why does the line with equation ax+by+c=0 has a negative slop is wrong? I get a and b<0 by -b/2a , is it correct to proof the values in this way? However, when I try to calculate its slope by -a/b, it is a negative slope. I have no idea why the above statement is wrong. Can anyone please teach me? Thank you]1

Answer 1

$a<0$ because of downward parabola.
$\frac{-2b}{2a}>0 \implies b>0$ by the $X$ co-ordinate of vertex. Now figure out the sign of slope of the straight line.
P.S. : You don't actually need sign of $a$ to figure out the sign of slope.