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# x, y intercepts

I have a math problem of x-y=4 . now how do you get 4 ordered pairs out of this. I could get to 2 but 4?

### Comments

The easiest way to come up with 4 ordered pair is to look at it as a simple subtraction problem. Example: pick any number to take the place of both X and Y to make it = 4.     4-0=4, 0- -4=4, 2- -2=4, 3- -1=4.
so your ordered pair are as follows.    (4,0)    (0,-4)    (2,-2)     (3,-1). Graph these points and where the two lines cross is your intercept.
There's a conflict in the question.  There's only 2 intercepts.  So does the problem ask for the intercepts, but you think there are 4 so you added that to the question?  Or is the problem actually asking for 4 ordered pairs, and you added intercept to the question when it doesn't say that?  It has to be one or the other.

There are only 2 intercepts (Vivien's answer), but there are an infinite number of ordered pairs, because you can plug in an infinite number of x's and solve for the corresponding y.  (Arthur's answer.)  If you really do need 4 coordinates, then you can pick any 4 x's you like and solve for the y that matches.  You can use the 2 intercepts as 2 of the 4 pairs.

### 3 Answers by Expert Tutors

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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If you are only looking for the x & y intercepts of the line x - y = 4, there is only one each, occurring at the two ordered pairs (0,-4) & (4,0).
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
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x-y=4
-y=-x+4
y=x-4
x=0,y=-4
x=1,y=-3
x=2,y=-2
x=3,y=-1
x=4,y=0
x=5,y=1
x=6,y=2
x=7,y=3
and so on...
x=-1,y=-5
x=-2,y=-6
x=-3,y=-7
and so on...
You have a straight line and the graph contains infinitely many points and therefore infinitely many ordered pairs: (0,-4), (1,-3), (2,-2), (3,-1), (4,0), (5,1), (6,2), (-1,-5), (-2,-6), ...
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi April;
You probably already know this...
The y-intercept is the value of y when x=0.
x-y=4
0-y=4
-y=4
y=-4
(0,-4)

The x-intercept is the value of x when y=0.
x-y=4
x-0=4
x=4
(4,0)

There is only one x-intercept.
There is only one y-intercept.