Question

What is the inequality that represents the graph shown?

Answer 1

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

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

`y-(-1)=(0-(-1))/(2-0)(x-0)`

`y+1=(1)/(2)x`

`y=(1)/(2)x-1`

The boundary line is a dashed line and the shaded portion is below the boundary line so the sign of inequality must be <.

`y<(1)/(2)x-1`

Therefore, the required inequality is
`y<(1)/(2)x-1`.