Chapter 6.5, Problem 38PPE

To determine

To find: If $(0,0)$ is used as a test point to determine shading portion, while graphing an inequality. Also how to choose a test point if $(0,0)$ is not a test point.

Answer to Problem 38PPE

  $(0,0)$ is not always used to determine where to shade. It is in case of when corresponding line already passes from $(0,0)$ . In this case to choose a test point, any point can be taken from any side of the line and the given linear inequality is got satisfied by that point. If inequality becomes true, shading goes on point`s side otherwise on other side of the line.

Explanation of Solution

Given information:

Any linear inequality is given that`s solution region to be satisfied by either point $(0,0)$ or if not then by any other point accordingly.

Concept used:

It is always a good practice to get a linear inequality satisfied by point $(0,0)$ . It is when line does not passes from origin or if the line is always of form $y=mx+c$ , related to given linear inequality. If line passes from origin then we pick any of the point from any side of this line, and get the linear inequality satisfied. If this point makes the inequality true, shading is done on this point`s side otherwise on other side of the line, related to given linear inequality.

Conclusion: So, if line does not passes from $(0,0)$ , use this point to choose shading and if line passes from this point, take any point that is not on this line to choose the shading..