Answer:
For two linear equations : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0;
To determine if two such straight lines are parallel, then you should check for the following conditions :
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ , where a,b are coefficients of x and y for each line.
if this condition is true for the coefficients of x,y, and the intercept of lines (c₁ and c₂) then they are parallel.
for instance,
let's say we have two lines :
x + 2y - 4 = 0,
2x + 4y - 12 = 0;
Now to check if they are parallel you simply check if the condition for parallel lines is met or not.
for these two lines :
a₁ = 1 , b₁ = 2, and c₁ = -4;
a₂ = 2, b₂ = 4, and c₂ = -12;
evaluating the values in the condition we have :
=
≠
;
since the condition for parallel is true for these two lines, we can conclude they are parallel.