The graph of a linear function f has a positive slope with intercepts (a,0) and (0,b), where a and b are non-zero integers. Which of the following statements about a and b could be true?

A) a + b = 0

B) a – 2b = 0

C) a = b

D) 0 <a < b

(I only know that Choice C is out because that would be true only if the slope=1 and the line passed through the origin, but since a and b are non-zero integers, there can be no point (0,0), so that one answer choice is out. )

It helps to do a bit of drawing here. Lines with positive slopes (that don’t pass through the origin) will always have either a positive *y*-intercept and a negative *x*-intercept, or a negative *y*-intercept and a positive *x*-intercept.

Therefore, you can eliminate choices B, C ,and D because in those answers, nonzero integers *a* and *b* must be the same sign. (Choice D goes further than B and C, requiring *a* and *b* to both be positive.) Choice A works because if *a* and *b* are nonzero, then they must have opposite signs for *a* + *b* = 0.