SOLUTION: How to determining at least three points thru which the graph passes? 1.) x+3=0 2.) 4x=y+3 3.) 2y=x-9 4.) 6x-3y=4 5.) x=3y

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Question 980315: How to determining at least three points thru which the graph passes?
1.) x+3=0
2.) 4x=y+3
3.) 2y=x-9
4.) 6x-3y=4
5.) x=3y
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
EASIEST WAY:
Pick a value for x (or for y , whichever makes it easier),
and then find the value of the other variable.

x%2B3=0 does not have a y ,
and that means that y can take any value it wants:
highlight%28y=anything%29 .
So we solve x%2B3=0 to find the value for x .
x%2B3=0--->x%2B3-3=0-3--->highlight%28x=-3%29 .
So, your three points could be (-3,0) , (-3,2) , and (-3,4),
or (-3,-10) , (-3,3) , and (-3,12),
or any three points with (-3,anything).

For 4x=y%2B3 ,
the easiest way is choosing values for x ,
and 0, 1, and 2 are easy numbers to work with.
Substituting the value x=0 we get
4%2A0=y%2B3--->0=y%2B3--->0-3=y%2B3-3--->-3=y ,
and that gives us the point (0,-3).
Substituting the value x=1 we get
4%2A1=y%2B3--->4=y%2B3--->4-3=y%2B3-3--->1=y ,
and that gives us the point (1,1).
Substituting the value x=2 we get
4%2A2=y%2B3--->8=y%2B3--->8-3=y%2B3-3--->5=y ,
and that gives us the point (2,5).
For +2y=x-9 and x=3y ,
I would choose values for y , because that will make it easier.

For +2y=x-9 , choosing 0, 1, and 2 for y we get:
Substituting the value y=0 we get
2%2A0=x-9--->0=x-9--->0%2B9=x-9%2B9--->9=x ,
and that gives us the point (9,0).
Substituting the value y=1 we get
2%2A1=x-9--->2=x-9--->2%2B9=x-9%2B9--->11=x ,
and that gives us the point (11,1).
Substituting the value y=2 we get
2%2A2=x-9--->4=x-9--->4%2B9=x-9%2B9--->13=x ,
and that gives us the point (13,2).

For x=3y , you can figure out what to do.

The graph 6x-3y=4 is a bit harder to do,
because choosing whole number values for one variable gives you fractional values for the other one.
Sometimes there is nothing better you can do.
I would make my life easier by choosing
x=0 for one point,
y=0 for another point,
and something else for a third point.
Substituting the value x=0 we get
6%2A0-3y=4--->0-3y=4--->-3y=4--->%28-3y%29%2F%28-3%29=4%2F%28-3%29--->y=-4%2F3 ,
and that gives us the point (0,-4/3).
Substituting the value y=0 we get
6x-3%2A0=4--->6x-0=4--->6x=4--->6x%2F6=4%2F6--->x=2%2F3 ,
and that gives us the point (2/3,0).
Then, substituting the value y=2 we get
6x-3%2A2=4--->6x-6=4--->6x-6%2B6=4%2B6--->6x=10--->6x%2F6=10%2F6--->x=5%2F3 ,
and that gives us the point (5/3,2).