Chapter 7.4, Problem 3E

Solution

Match the inequality with the graphs and indicate whether the boundary is included or excluded from the graph.

Graph (b); Boundary is included from the graph.

Given Information:

The inequality is $2x-5y\ge 2$ .

Explanation:

Consider the given inequality, $2x-5y\ge 2$ .

Rewrite the given inequality,

  $\begin{array}{c}2x\ge 5y+2\\ x\ge \frac{5}{2}y+1\end{array}$

Write the equation of the obtained inequality by replacing the sign “ $\ge$ ” with the “ $=$ ”. The inequality sign $\ge$ will indicate that the graph should be drawn with a solid line.

The obtained equation will be $x=\frac{5}{2}y+1$ .

Check for the point $\left(5,-5\right)$ if it satisfies the inequality.

  $\begin{array}{l}5\stackrel{?}{\ge }\frac{5}{2}\left(-5\right)+1\\ 5\stackrel{?}{\ge }-12.5+1\\ 5\ge -11.5\end{array}$

Draw the graph of $x\ge \frac{5}{2}y+1$ .

  

The graph of $2x-5y\ge 2$ is the graph consisting of all the points on and below the line $x=\frac{5}{2}y+1$ .

Therefore, the given inequality matches with the graph (b) and boundary is included from the graph.