Chapter 5.6, Problem 37E

To determine

To write: an inequality for its given graph.

Answer to Problem 37E

  $y\le -\frac{1}{2}x-2.$

Explanation of Solution

Given information: We have given an inequality graph:

  

Solution:

From the graph, we can see that the line crosses at the y -axis at -2.

So, the y -intercept (b) = -2.

If we go 1 unit downward and 2 unit right then we get a point (2, -3).

Therefore, $\frac{Rise}{Run}=\frac{-3-\left(-2\right)}{2-0}=-\frac{1}{2}$

So, the slope (m) of line is $-\frac{1}{2}$ .

Now, plug the values of slope ( m ) = $-\frac{1}{2}$ and y -intercept ( b ) = -2 in slope intercept form $y=mx+b$ .

  $y=\left(-\frac{1}{2}\right)x+\left(-2\right)$

  $y=-\frac{1}{2}x-2$

The line in our graph is solid. This means our inequality will include either $\ge$ or $\le$ .

We can see that the area "below" our line is shaded. This means that the solutions are smaller or equal than the points on the line. For shade down we use $\le$ inequality sign.

Therefore, the inequality for given graph is:

  $y\le -\frac{1}{2}x-2.$