Question

What is the Inequality for this graph?

Answer 1

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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-0=\dfrac{-4-0}{0-6}(x-6)$

$y=\dfrac{-4}{-6}(x-6)$

$y=\dfrac{2}{3}(x-6)$

$y=\dfrac{2}{3}x-4$

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 <.

$y$

Therefore, the required inequality for the given graph is $y$.