Mathematic...?

Question

it is given that a,b, and c satisfy the following conditions:
i) abc is not equal to 0
ii) (a+b)/c = (b+c)/a = (a+c)/b = p
prove that the straight line y=px+p passes through the 2nd and 3rd quadrants.

Answer 1

If p is not equal to 0, then the line
y = px + p
always crosses the x-axis at (-1,0), so it must pass into both the 2nd and 3rd quadrants.

a, b, c are irrelevant to this conclusion.

Answer 2

Solution of equatios (ii) is a = b = c ≠ 0
=> p = 2
=> Equation of line is y = 2x + 2
=> for ngative values of x, y can be positive or negative, e.g.,
x = -1/2 => y = 1 and x = -2 => y = -2
Thus, there are points on the line which can be in the 2nd and 3rd quadrants.
Hence, the line y = px + p passes through the 2nd and 3rd quadrants.

Answer 3

a=b=c so p = a positive number
Therefore slope is positive and y-intercept is positive
Therefore the line y = px+p must pass through Quadrants III, II, and I.