Given:
The graph of an inequality.
To find:
The inequality for the given graph.
Solution:
From the given graph it is clear that the boundary line passes through two point (0,3) and (2,4). So, the equation of boundary line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-3=\dfrac{4-3}{2-0}(x-0)[/tex]
[tex]y-3=\dfrac{1}{2}(x)[/tex]
[tex]y=\dfrac{1}{2}x+3[/tex]
The shaded area lies below the boundary line and the boundary line is a solid line. So, the sign of inequality must be ≤.
The required inequality is
[tex]y\leq \dfrac{1}{2}x+3[/tex]
Therefore, the correct option is B.
