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