SOLUTION: determine whether each pair of equations represents parallel lines: y=-3x+1, 6x+2y=8

There are several ways to do this. Pick whichever way
your teacher told you to use.

Method 1:  Put them both in slope-intercept form. If 
their slopes are equal, but they have different 
y-intercepts, then they are parallel.

Method 2:  Choose any two values for x.  Substitute 
           them both in each equation to find the 
           y-values corresponding to them.  If the 
           corresponding y-values have the same non-zero
           difference, then the lines are parallel.

Method 3:  Put them both in general form. Then 



if  then they are parallel.   

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Method 1:  



The first one is already in the slope intercept form
.  Get the second one in slope-intercept 
form, by solving for y



Add  to both sides:



Divide every term by :





So the slope is the coefficient of x, which is -3
So the value of the slope  is the same in 
both equations, but their y-intercepts are different.
Therefore the lines those equations
represent are parallel.

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Method 2:



Substitite x=0 in each and solve for y:

In the first one:

  



In the second one:







Subtract them, second y - first y = 

Substitite x=1 in each and solve for y:

In the first one:

  




In the second one:







Subtract them, second y - first y = 

We get the same difference 3, so the lines represented
by those equations are parallel.

------------------------------------------------

Method 3:



Get the forst one in general form:




So the system is now:



See if the coefficients of x and y are in
the same proportion:

Is  true?

Yes it is, therefore the lines those equations
represent are parallel.

Edwin