Chapter 7, Problem 81RE

To determine

Tocalculate: Write a system of inequalities to describe the region of rectangle with given vertices

Answer to Problem 81RE

  $y\ge 0$

Explanation of Solution

Region of a rectangle with vertices at $\left(3,1\right),\left(7,1\right),\left(7,10\right)$ and $\left(3,10\right)$ .

Therefore, the graph of function passes through the points $\left(3,1\right),\left(7,1\right),\left(7,10\right)$ and $\left(3,10\right)$ .

From the points observation and given information,

The vertices of x will vary between $3$ and $7$ .

That is $x\ge 3andx\le 7$ .

And the vertices of $y$ will vary between $1$ and $10$ .

That is $y\ge 1andy\le 10$ .

Slope of line

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{1-1}{7-3}\\ =0\end{array}$

Therefore $y=0$

And the inequality of $y$ will be written as: $y\ge 0$