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.