Question

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?

Answer 1

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