Question

Which of the following inequalities is shown in the graph?

Answer 1

Point (0,0) lies on the shaded region.The shaded region lies below the line.

Putting ,x=0 and y=0 , from option(Inequality) 1 to 4

Option 1

 0 ≤ -2-----Incorrect

Option 2

0 ≤ 0.5-----Correct

Option 3

0 ≤ 0.5 -------Correct

Option 4

0 ≥ 0.5 -------Incorrect

Origin(0,0) Satisfy Inequality 2 and Inequality 3.

Equation of line cuts Positive x and positive y axis.Also, angle made by line with positive Direction of X axis is Positive.

So, Tangent of Angle will be Positive.

Option 3 ,that is Inequality 3,  satisfies the shaded region.

   $y\leq 2x+\frac{1}{2}$

Answer 2

The following inequality shown is 2) because the y-intercept is at 1/2 and the slope is negative. The graph is also shaded underneath so must include the values underneath the function