Question

Which linear inequality represents the graph below?

Answer 1

Given:

The graph of an inequality.

To find:

The inequality.

Solution:

In the given graph, the boundary line passes through the points (-3,3) and (0,1).

So, the equation of the boundary line is:

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

$y-3=\dfrac{1-3}{0-(-3)}(x-(-3))$

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

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

Adding 3 on both sides, we get

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

$y=-\dfrac{2}{3}(x)+1$

The boundary line is a solid line and the shaded region is above the boundary line. So, the sign of inequality must be $\geq$ and the required inequality is:

$y\geq -\dfrac{2}{3}(x)+1$

Therefore, the correct option is B.