Chapter 6.4, Problem 46SR

To determine

Graph the inequality $y>\frac{1}{2}x+3$ .

Explanation of Solution

Given:

The inequality is $y>\frac{1}{2}x+3$ .

Calculation:

Simplify the inequality as follows:

  $\begin{array}{l}y>\frac{1}{2}x+3\\ 2y-x>6\end{array}$

Thus, the graph of $2y-x=6$ ,

Consider x = 0,

  $\begin{array}{l}2y-0=6\\ y=3\end{array}$

Thus, the coordinate is (0, 3).

Consider y = 0,

  $\begin{array}{c}2\left(0\right)-x=6\\ x=-6\end{array}$

Thus, the coordinate is (-6, 0).

The graph of the line is shown below:

  

Apply the inequality in the graph on the upside of the graph as inequality is greater than. Also, change the solid line to dashed line.