Given:
The graph of an inequality.
To find:
The inequality that represents the graph shown.
Solution:
From the given graph it is clear that the boundary line passes through the points (0,-1) and (2,0). 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-(-1)=\dfrac{0-(-1)}{2-0}(x-0)[/tex]
[tex]y+1=\dfrac{1}{2}x[/tex]
[tex]y=\dfrac{1}{2}x-1[/tex]
The boundary line is a dashed line and the shaded portion is below the boundary line so the sign of inequality must be <.
[tex]y<\dfrac{1}{2}x-1[/tex]
Therefore, the required inequality is [tex]y<\dfrac{1}{2}x-1[/tex].
