SOLUTION: reasonableness: Which of the following order pairs is not included on the graph equation y=x+9 (7,16) (15,24)(20,29) (28,36)

Let's check to see if (7,16) is included on the graph of y-x+9.  
The first coordinate of (7,16) is 7. That's the x-coordinate, 
so that's what we substitute for x.  So instead of the x in y=x+9 
we will substitute 7.

The second coordinate of (7,16) is 16. That's the y-coordinate, 
so that's what we substitute for y.  So instead of the y in y=x+9 
we will substitute 16.

So 

y=x+9

becomes

16=7+9

and when we add 7+9 we get 16, so we end up with

16=16

So (7,16) is included on the graph of y=x+9

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

Next let's check to see if (15,24) is included on the graph of y-x+9.  
The first coordinate of (15,24) is 15. That's the x-coordinate, 
so that's what we substitute for x.  So instead of the x in y=x+9 
we will substitute 15.

The second coordinate of (15,24) is 24. That's the y-coordinate, 
so that's what we substitute for y.  So instead of the y in y=x+9 
we will substitute 24.

So 

y=x+9

becomes

24=15+9

and when we add 15+9 we get 24, so we end up with

24=24

So (15,24) is included on the graph of y=x+9

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

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

Next let's check to see if (20,29) is included on the graph of y-x+9.  
The first coordinate of (20,29) is 20. That's the x-coordinate, 
so that's what we substitute for x.  So instead of the x in y=x+9 
we will substitute 20.

The second coordinate of (20,29) is 29. That's the y-coordinate, 
so that's what we substitute for y.  So instead of the y in y=x+9 
we will substitute 29.

So 

y=x+9

becomes

29=20+9

and when we add 20+9 we get 29, so we end up with

29=29

So (20,29) is included on the graph of y=x+9

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

Finally let's check to see if (28,36) is included on the graph of y-x+9.  
The first coordinate of (28,36) is 28. That's the x-coordinate, 
so that's what we substitute for x.  So instead of the x in y=x+9 
we will substitute 28.

The second coordinate of (28,36) is 36. That's the y-coordinate, 
so that's what we substitute for y.  So instead of the y in y=x+9 
we will substitute 36.

So 

y=x+9

becomes

36=28+9

and when we add 28+9 we get 37, so we end up with

36=37

That's FALSE!  So (28,36) is NOT included on the graph of y=x+9

So the answer is (28,36).

Here's what we have shown about the graph.  The black line below
is the graph of y=x+9, and you see that all the ordered pairs given
represent points that are included in the line graph except (28,36),
which is not on the line.



Edwin