# LINR 2 | Lesson 3 | Explore 1

A linear inequality divides the plane into 3 parts: the line, and the regions on either side of the line. In the graph above, the line can be represented by

$2x-3y=-6 \, \text{ or } \, y=\frac{2}{3} \normalsize x+2$

How do we decide between $$\leq$$, <, >, $$\geq$$?

One student decided that $$2x-3y>-6$$ because the shading is above the line. How can we tell if she was correct?

Go to Desmos, graph the line $$2x – 3y = 6$$

Choose a test point in each of the regions.

Choose a point in the plane. For example, $$(-3,\,4)$$

Is the point in the solution region?

Yes, so when I substitute in $$2x-3y>-6$$, my resulting inequality should be true:

$$2x-3y>-6$$ ? for $$(-3,\,4)$$

Try a few test points in each region and a point on the line to verify.