Answer:
Option C
Step-by-step explanation:
As you can see in the graph the shaded region is in 1st quadrant which means that both x and y are greater than or less than equal to zero. From this statement only option A and B get eliminated. But still we will look further...
The equation of the yellow line should be determined in order to know the complete answer. If you don't know how to write equation of line in intercept form then just assume the line's equation to be :
y=mx + c ; where m and c are constants.
Now you just need to find two points satisfying the line's equation. As you can see in the graph (2,0) and (0,-2) are the points lying on the line. Now put them in the assumed line's equation to determine the constants.
0 = m × 2 + c .........equation (1)
-2 = m × 0 + c .........equation (2)
solving equation (2) gives c = -2
put the value of c in equation (1) then solve it to get the value of m
0 = m × 2 - 2
m=1
Therefore line's equation is y = x - 2
Since the value of y is greater than and equal to the value of y which we get from the line's equation so
y ≥ x - 2
rearrange the above inequality
x - y ≤ 2
So these three conditions are there
x ≥ 0
y ≥ 0
x - y ≤ 2
which gives the shaded region
