Which inequality is represented by the graph?
a) y≥−12x+2.5
b) y> −2x+2.5
c) y≥−2x+2.5
d) y≤−2x+2.5

Option C.

Step-by-step explanation:

If a line passes through two points and , then the equation of line is

From the given graph it is clear that the related line passes thorough the points (0,2.5) and (2,-1.5).

The equation of related line is

Add 2.5 on both sides.

Th sign of inequality is either ≤ or ≥ because the related line is a solid line. It means the points on the line are included in the solution set.

Let the required inequality is

(1,1) is included in the shaded region. So, the above inequality is true for (1,1).

The assumed inequality is true for (1,1). So, the required inequality isn .

Therefore, the correct option is C.