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=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-0=(-4-0)/(0-6)(x-6)`

`y=(-4)/(-6)(x-6)`

`y=(2)/(3)(x-6)`

`y=(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<(2)/(3)x-4`

Therefore, the required inequality for the given graph is
`y<(2)/(3)x-4`.