Chapter 11, Problem 68RE

To determine

The intercepts an then plot the intercept on the graph of the plane.

Explanation of Solution

Given:

The expression is given as:

  $5x-y-5z=5$

For determining the x intercept, the y and z should be equal to the 0.

Hence,

  $\begin{array}{l}5x-y-5z=5\\ 5x-0-5\left(0\right)=5\\ x=1\end{array}$

Therefore, the x intercept is (1,0,0).

Now, similarly for y-intercept the value of the x and z should be equal to the 0.

  $\begin{array}{l}5x-y-5z=5\\ 5\left(0\right)-y-5\left(0\right)=5\\ y=-5\end{array}$

Therefore, the y-intercept is (0,-5,0).

Similarly, the z-intercept:

  $\begin{array}{l}5x-y-5z=5\\ 5\left(0\right)-0-5z=5\\ z=-1\end{array}$

Therefore, the z intercept is (0,0,-1).

Now, the equation of the plane can be expressed as:

  $\begin{array}{l}5x-y-5z=5\\ -5z=5+y-5x\\ z=\frac{-5+5x+y}{5}\end{array}$

Using the Maple system to draw the graph for the above equation: