SOLUTION: the two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are identical if

Question 984646: the two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are identical if
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the equations are multiples of each other.

an example:

x + y + 3 = 0
2x + 2y + 6 = 0

these equations are multiples of each other.

convert each equation to slope intercept form of y = mx + b.
m is the slope.
b is the y-intercept.

start with x + y + 3 = 0
subtract x from both sides and subtract 3 from both sides to get:
y = -x - 3

start with 2x + 2y + 6 = 0
subtract 2x from both sides and subtract 6 from both sides to get:
2y = -2x - 6
divide both sides by 2 to get:
y = -x - 3

in slope intercept form the two equations are identical.
first equation is:
y = -x - 3
second equation is:
y = -x - 3

the slope intercept form of the equation is y = mx + b where m is the slope and b is the y-intercept.

both equations have the same slope (-1) so they are either parallel or identical.

both equation have the same y-intercept so they are identical.

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.

those are the rules.

Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!

The two lines    and    are identical if

= =     or

= = .

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