Answer:
The equation of the line is y + x + 1 = 0.
Step-by-step explanation:
The given equations are : x + 2y = 0 and 3x + y + 5 = 0
Now, finding the intersection point of the above system:
from (1) , x = -2y
put in (2), 3 (-2y) + y + 5 = 0
or, 5y = 5 ,or y = 1
If y = 1, pitting in (1), x = -2
So, the intersection lines is (-2,1).
the other point on line is (-3,2)
Now, finding the slope m of the line :
or, = -1
So, by POINT SLOPE FORM: the equation of a line is
(y - y0) =m (x -x0),
now for (-3,2) : equation is ( y - 2) = (-1) (x +3)
or, y + x + 1 = 0
Hence, the equation of the line that passes through (−3, 2) and the intersection of the lines x+2y=0 and 3x+y+5=0 is y + x + 1 = 0.