Question 197445
<font size = 8 color = "red"><b>Edwin's explanation:</b></font>
Please show me step by step to graph

{{{3x+2y=6}}}

thank you
<pre><font size = 4 color = "indigo"><b>
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+2y=6}}}
{{{3(0)+2y=6}}}
{{{0+2y=6}}}
{{{2y=6}}}
{{{(2y)/2=6/2}}}
{{{cross(2)y/cross(2)=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+2y=6}}}
{{{3x+2(0)=6}}}
{{{3x+0=6}}}
{{{3x=6}}}
{{{(3x)/3=6/3}}}
{{{cross(3)x/cross(3)=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+2y=6}}}
{{{3(1)+2y=6}}}
{{{3(1)+2y=6}}}
{{{3+2y=6}}}
{{{2y=3}}}
{{{(2y)/2=3/2}}}
{{{cross(2)y/cross(2)=3/2}}}
{{{y=3/2}}}
{{{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:

{{{drawing(400,400,-5,5,-5,5, graph(400,400,-5,5,-5,5),
line(-.1,3,.1,3), line(0,2.9,0,3.1),line(-.1,2.9,.1,3.1),line(-.1,3.1,.1,2.9),
line(1.9,0,2.1,0), line(2,-.1,2,.1),line(1.9,-.1,2.1,.1),line(1.9,.1,2.1,-.1) 
line(.9,1.5,1.1,1.5), line(1,1.4,1,1.6),line(.9,1.4,1.1,1.6),line(.9,1.6,1.1,1.4)
)}}}

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

{{{drawing(400,400,-5,5,-5,5, graph(400,400,-5,5,-5,5,(-3/2)x+3),
line(-.1,3,.1,3), line(0,2.9,0,3.1),line(-.1,2.9,.1,3.1),line(-.1,3.1,.1,2.9),
line(1.9,0,2.1,0), line(2,-.1,2,.1),line(1.9,-.1,2.1,.1),line(1.9,.1,2.1,-.1) 
line(.9,1.5,1.1,1.5), line(1,1.4,1,1.6),line(.9,1.4,1.1,1.6),line(.9,1.6,1.1,1.4)
)}}}

Edwin</pre>