dave13 wrote:
mymbadreamz wrote:
Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?
A. y=x
B. y=x+1/2
C. Y=x+5
D. y=x*1/2
E. y=x/2 +5
Bunuel 
what does this question want?
I cant understand ...
, I'm just expanding a little on the two excellent answers above, because you mentioned that you knew this slope-intercept equation for a line.
y's value depends on x. For every x, there is only one y.
So you can plug in an integer for x, as
Bunuel and
pushpitkc noted, and get a y value.*
The result for each option, as
abhimahna noted, will give you a point on the line as if it were graphed. As he also noted, one of the answers' coordinates, if graphed, will NOT be (x,y) = (integer, integer)
For options B, D, and E, which have x/2, try x = 0 and x = 2 (or any even integer).
Is y an integer?
For A and C, you can use x = 0 (or just note that y = b). Is y an integer?
Answer B will never yield (x,y) = (integer, integer).
Answer B) y = x + 1/2
x = 0, y = 1/2 (y = b)
x = 1, y = 1 1/2
x = 2, y = 2 1/2
As
Bunuel and
pushpitkc explain, adding 1/2 to integer x will never yield y = integer.
Answer B
* In all the equations, some of the x values will not be integers. Example: y = x. If x = 1/2, y = 1/2. But if x = 0,1,2,3 etc., y = 0,1,2,3. Those coordinates ARE (integer, integer). Not what the prompt wants.
In one of the equations, however, when x IS an integer, y can never be an integer. In all the other equations, you can find an x value whose y value IS an integer. If you can find a y value that is an integer, that answer is disqualified.
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-- Albert Camus, "Return to Tipasa"
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76% (00:38) correct 
