Question

Determine quadrant using slope of a line

Answer 1

Suppose there's a line whose equation is ax + by +c = 0

then , it's slope gonna be = m = tan θ = -b/a

So value of slope (a & b) determines tanθ and thus the angle between line and x axis.

Case1)  when slope is positive .

Either a is positive and b is negative Or b is positive and a is negative.

eg.  y-x +1 = 0   ⇒ line makes acute angle with x axis .

Case 2) when slope is negative

Either both a & b positive Or both negative

Eg. x+2y +5=0     ⇒ line makes obtuse angle with x axis .

Now you are inquiring regarding the quadrant of line, that make no sense.
Cause line could be present in any of the quadrants.It extends to infinity.
Yes in case you are asking about the quadrants of points, that could be tell.

If x is positive and y too positive then, 1st quadrant.
If x's negative and y pos. then , its 2nd.
If both negative then, then it got be 3rd .
And if x is pos. and y is neg. then , its 4th quadrant.

If any queries , do ask.