Chapter 5.6, Problem 36E

To determine

To write: an inequality for its given graph.

Answer to Problem 36E

  $y=\frac{1}{2}x+2.$

Explanation of Solution

Given information: We have given an inequality graph:

  

Determine the equation of line:

From the graph, we can see that the line crosses the y -axis at (0, 2).

So, the y -intercept (b) = 2

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

Now, let us find the slope

  $Slope=\frac{Rise}{Run}=\frac{3-2}{2-0}=\frac{1}{2}$

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

Plug the value of slope ( m ) and y -intercept ( b ) in slope intercept form $y=mx+b$ .

  $y=\left(\frac{1}{2}\right)x+2$

  $y=\frac{1}{2}x+2$

The line in our graph is dotted. This means our inequality will include either > or <.

We can see that the area "above" the dotted line is shaded. That means the solutions are greater than the points on the line. For shade up we use > sign.

Therefore, the inequality is:

  $y=\frac{1}{2}x+2.$