SOLUTION: complete the ordered pairs for the given equation: 7x+3y=21 (0, ),( ,0),(6, ),( ,14)

We are given the first coordinate 0 and we are asked to find the 
second coordinate.  The first coordinate is what we substitute
for x, so we will substitute 0 for x in

  7x+3y = 21  and solve for the other letter y:

7(0)+3y = 21
   0+3y = 21
     3y = 21
      y = 7

So the first one is (0,7)

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We are given the second coordinate 0 and we are asked to find the 
first coordinate.  The second coordinate is what we substitute
for y, so we will substitute 0 for y in

  7x+3y = 21  and solve for the other letter x:

7x+3(0) = 21
   7y+0 = 21
     7y = 21
      y = 3

So the second one is (3,0)

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We are given the first coordinate 6 and we are asked to find the 
second coordinate.  The first coordinate is what we substitute
for x, so we will substitute 6 for x in

  7x+3y = 21  and solve for the other letter y:

7(6)+3y = 21
  42+3y = 21
     3y = -21
      y = -7

So the third one is (6,-7)

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We are given the second coordinate 14 and we are asked to find the 
first coordinate.  The second coordinate is what we substitute
for y, so we will substitute 14 for y in

   7x+3y = 21  and solve for the other letter x:

7x+3(14) = 21
   7y+42 = 21
      7y = -21
       y = -3

So the last one is (-3,14)

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Now we'll plot those ordered pairs as points:

 (0,7), (3,0), (6,-7), (-3,14)  

and this is what we see on the left, and on the right 
we see that they all line up so that we can get a ruler 
and draw a straight line through all of those points
represented by those ordered pairs.

        

Edwin