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

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

$y-(-1)=\dfrac{0-(-1)}{2-0}(x-0)$

$y+1=\dfrac{1}{2}x$

$y=\dfrac{1}{2}x-1$

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

$y$

Therefore, the required inequality is $y$.