If two lines, written in standard form, are a1x + b1y = c1 and a2x = b2y = c2, what is the relationship of a1, a2, b1, and b2 if the lines are parallel?

hello:

a1x + b1y = c1 ... (1)

a2x = b2y = c2, ... (2)

the lines are parallel when has same slope

calculate the slope of the line (1):

a1x + b1y = c1

b1y = c1 - a1x

if : b1 ≠ 0 : y = (-a1/b1) x + c1/b1

the slope is : - a1/b1

same method the slope of the line (2) is : - a2/b2

the relationship of a1, a2, b1, and b2 if the lines are parallel is:

-a1/b1 = - a2/b2