Question

two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are parallel if​

Answer 1

Step-by-step explanation:

the equations are multiples of each other. equations are identical if they have the same slope and the same y-intercept. ... equations are parallel if they have the same slope and different y-intercepts.

hope it is helpful

Answer 2

Answer:

Concept:
If two lines have different y-intercepts and equal slopes, they are said to be parallel. Slopes of Perpendicular Lines. In other words, the reciprocals of perpendicular slopes are negative.

Step-by-step explanation:

Given:

Two lines
$a_{1} x+b_{1} y+c_{1}=0\\a_{2} x+b_{2} y+c_{2}=0$    are parallel  if

Solution:

When two lines are parallel, both are either vertical or non-vertical. If both are vertical, then b1 = b2 = 0 so that a1b2 = a2b1 = 0. If both are non-vertical, their slopes are equal.

Thus  - a1/b1 = -a2/b2

Hence,   a1b2 = a2b1  or  a1:b1 = a2:b2

Conversely, when a1b2 = a2b1 and if b1 = 0, then a1 ≠ 0 so that b2 = 0. Therefore, b1 = 0 ⇔ b2 = 0, and hence if one of the lines is vertical, then the other is also vertical so that the given lines are parallel. If both b1 and b2 are non-zero, then  Since the slopes are equal, the lines are parallel.

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