Exercise 23 Page 403

There are two major steps to writing an inequality when given its graph.

1. Write an equation for the boundary line.
2. Determine the inequality symbol and complete the inequality.

In this exercise we have been given a system consisting of two linear inequalities. We will tackle them one at a time and bring them together in a system at the end.

The Blue Region

It only takes two points to create a unique equation for any line, so let's start by identifying two points on the boundary line.

Here we have identified two points, $(\text{-}3,1)$ and $(0,0),$ and indicated the horizontal and vertical changes between them. This gives us the $\text{rise}$ and $\text{run}$ of the graph, which will give us the slope $m.$ One of the points we selected, $(0,0),$ is also the $y\text{-}$intercept. With slope $m$ and the $y\text{-}$intercept at the point $(0,b),$ we can write an equation for the boundary line in slope-intercept form.