Answer:
Ax + Ay + 2A = 0 for any nonzero A, for example (A=1): x + y + 2 = 0
Step-by-step explanation:
The equation of a line is
Ax + By + C = 0
so we know that:
A*-3 + B*1 + C = 0
A*5 + B*-7 + C = 0
Let's subtract one from the other:
A*(-3 - 5) + B*(1 + -7) = 0
A*-8 + B*8 = 0
B*8 = A*8
B = A
Let's input B = A into the first two equations
A*-3 + A*1 + C = A*-2 + C = 0
A*5 + A*-7 + C = A*-2 + C = 0
checks out
C = 2A
So for any nonzero A the equation of
Ax + Ay + 2A = 0 produces a line passing between the points. Example would be
x + y + 2 = 0
