Which linear inequality is shown on the graph? a) x − y ≤ −2 b) x − y ≥ −2 c) x − y ≤ 2 d) x − y ≥ 2

choice C) x-y <= 2



Explanation:

The two points (0,-2) and (2,0) are on the boundary line. The boundary line equation is y = x-2. We find this equation through the use of the slope formula to find that m = 1. The y intercept is -2 so b = -2. Therefore, y = mx+b turns into y = 1x+(-2) which simplifies to y = x-2

The equation y = x-2 can be arranged to get x-y = 2 (subtract y from both sides; add 2 to both sides)

So the answer is either x-y <= 2 OR it is x-y >= 2

The question is: which inequality has the test point (0,0) in it? We pick on the origin since 0 is the easiest number to work with.

Plug (x,y) = (0,0) into the equation for choice C
x-y <= 2
0-0 <= 2
0 <= 2
which is true. So choice C is the answer.

Choice D can be ruled out since...
x-y >= 2
0-0 >= 2
0 >= 2
which is false: 0 is not larger or equal to 2