we Know that
The formula to calculate the slope between two points is equal to

Let

substitute the values in the formula



therefore
the answer is the option

We can use elimination to solve the system:
x+2y=0 Multiply the first equation by negative 2 so we can eliminate
2x+4y=0
-2-4y=0 Add them, -2X+2X= 0, -4Y+4Y= 0
2x+4y=0
0=0
Since 0 is indeed equal to 0 you have INFINITELY MANY SOLUTIONS.
you could also put both equation in slope intercept form and see if the slopes and Y-intercept are the same.