Question 984646
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.