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 the points (6,0) and (0,-4). So, the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-0=\dfrac{-4-0}{0-6}(x-6)[/tex]
[tex]y=\dfrac{-4}{-6}(x-6)[/tex]
[tex]y=\dfrac{2}{3}(x-6)[/tex]
[tex]y=\dfrac{2}{3}x-4[/tex]
The area under the boundary line is shaded and boundary line is a dotted line it means the points on the line are not included in the solution set. So, the inequality sing must be <.
[tex]y<\dfrac{2}{3}x-4[/tex]
Therefore, the required inequality for the given graph is [tex]y<\dfrac{2}{3}x-4[/tex].
