SOLUTION: Please show me step by step to graph 3x+2y=6 thank you

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Question 197445: Please show me step by step to graph

3x+2y=6

thank you
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B2y=6 Start with the given equation.


2y=6-3x Subtract 3x from both sides.


2y=-3x%2B6 Rearrange the terms.


y=%28-3x%2B6%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%28-3%29%2F%282%29%29x%2B%286%29%2F%282%29 Break up the fraction.


y=-%283%2F2%29x%2B3 Reduce.




Looking at y=-%283%2F2%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-3%2F2 and the y-intercept is b=3


Since b=3 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -3%2F2, this means:

rise%2Frun=-3%2F2


which shows us that the rise is -3 and the run is 2. This means that to go from point to point, we can go down 3 and over 2



So starting at , go down 3 units


and to the right 2 units to get to the next point



Now draw a line through these points to graph y=-%283%2F2%29x%2B3

So this is the graph of y=-%283%2F2%29x%2B3 through the points and

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's explanation:
Please show me step by step to graph
3x%2B2y=6
thank you

Find three points.  Actually two points is enough, as Jim Thompson
has shown you in his good explanation. Trouble is, any two points 
are such that a straight line can be drawn through both of them.  
And since people sometimes make mistakes we should get a third 
point as a check.  Then if you can't draw a straight line through 
all three of them, then you would know that there is a mistake in 
one of the three.

Let's make this table: 

  x | y | (x,y) 
 ---------------
    |   | ( , ) 
 --------------- 
    |   | ( , )
 ---------------
    |   | ( , )

Let's choose 0 for x for one point and choose 0 for y 
for a second point.  Such points are called the
"intercepts".


Then for the third check point we can choose any number 
positive or negative.  I'll arbitrarily choose 1 for x,
but you could choose any number for x or y.

  x | y | (x,y) 
 ---------------
  0 |   | (0, ) 
    | 0 | ( ,0)
  1 |   | (1, )

To find the value of y that corresponds to x=0, we substitute
0 for x in the equation:

3x%2B2y=6
3%280%29%2B2y=6
0%2B2y=6
2y=6
%282y%29%2F2=6%2F2
cross%282%29y%2Fcross%282%29=3
y=3

So we fill in 3 for y, and we have:

  x | y | (x,y) 
 ---------------
  0 | 3 | (0,3) 
    | 0 | ( ,0)
  1 |   | (1, )

To find the value of x that corresponds to y=0, we substitute
0 for y in the equation:

3x%2B2y=6
3x%2B2%280%29=6
3x%2B0=6
3x=6
%283x%29%2F3=6%2F3
cross%283%29x%2Fcross%283%29=2
x=2

So we fill in 2 for x, and we have:

  x | y | (x,y) 
 ---------------
  0 | 3 | (0,3) 
  2 | 0 | (2,0)
  1 |   | (1, )

To find the value of x that corresponds to x=1, we substitute
1 for x in the equation:

3x%2B2y=6
3%281%29%2B2y=6
3%281%29%2B2y=6
3%2B2y=6
2y=3
%282y%29%2F2=3%2F2
cross%282%29y%2Fcross%282%29=3%2F2
y=3%2F2
y=1.5

So we fill in 1.5 for x, and we have:

   x  |  y  | (x,y) 
 -------------------
   0  |  3  | (0,3)   
   2  |  0  | (2,0)   
   1  | 1.5 | (1,1.5)

   x  |  y  | (x,y) 
 -------------------
   0  |  3  | (0,3)   <--- that's the y-intercept 
   2  |  0  | (2,0)   <--- that's the x-intercept
   1  | 1.5 | (1,1.5)


Now we plot those three points:



Now we take a ruler and draw a line through them:



Edwin