Chapter 7, Problem 68RE

To determine

Sketch the graph of the inequality.

Answer to Problem 68RE

The point $\left(-1,2\right)$ , $\left(0,3\right)$ is satisfies the inequality.

Explanation of Solution

Given information:

Sketch the graph of the inequality.

  $3y-x\ge 7$

Calculation:

Consider the inequality,

  $3y-x\ge 7$

To solve for $y$ add $x$ both sides.

  $\begin{array}{l}3y-x+x\ge 7+x\\ 3y\ge 7+x\\ y\ge \frac{7+x}{3}\end{array}$

Now sketch the graph for equation $y=\frac{7+x}{3}$

Use MAPLE to plot of equation $y=\frac{7+x}{3}$

Feed the equation and do right click,

  

Now consider test points

1. On the line
2. Below the line
3. Above the line

Consider point $\left(-1,2\right)$ on the line,

  $\begin{array}{l}y=\frac{7+x}{3}\\ =\frac{7-1}{3}=2\\ y=2\end{array}$

This satisfy the inequality

Consider point $\left(0,0\right)$ below the line,

  $\begin{array}{l}y=\frac{7+x}{3}\\ =\frac{7+0}{3}=\frac{7}{3}\\ y>\frac{7}{3}\end{array}$

This does not satisfy the inequality.

Consider point $\left(0,3\right)$ above the line

  $\begin{array}{l}y=\frac{7+x}{3}\\ =\frac{7+0}{3}=\frac{7}{3}\\ y>\frac{7}{3}\end{array}$

This satisfy the inequality

Hence the graph of inequality $3y-x\ge 7$ above and on the line.

  

Let us take the point $\left(0,0\right)$ from lower plane,

Hence, the point $\left(-1,2\right)$ , $\left(0,3\right)$ is satisfies the inequality.