# liner inequalities

• Oct 10th 2006, 11:51 PM
robpez
liner inequalities
could some one show me the easiest way to graph liner inequalities like this
Also what if the problem has two inequalities for one question

problem 2x + 5y > -10
• Oct 11th 2006, 12:19 AM
CaptainBlack
Quote:

Originally Posted by robpez
could some one show me the easiest way to graph liner inequalities like this
Also what if the problem has two inequalities for one question

problem 2x + 5y > -10

First draw the boundary curve (or curves for multiple inequalities), in this
case:

2x + 5y = -10.

Then shade the region on the side of the boundary curve for which the
inequality holds, in this case the region above the line.

(in the case of multiple inequalities the region over which they all hold
is the intersection of the individual regions over which they individualy hold).

RonL

RonL
• Oct 11th 2006, 05:52 AM
Soroban
robpez!

Quote:

Could some one show me the easiest way to graph linear inequalities like this:
. . 2x + 5y > -10

Also what if the problem has two inequalities for one question?

As the Captain suggested, graph the equality (line).

The line: .2x + 5y .= .-10 .has intercepts (-5,0) and (0,-2) **
Graph this line . . . use a dotted line since it is not included in the solution.

Solve the inequality for y (carefully!)
. . 2x + 5y .> .-10
. . . . . .5y .> .-2x - 10
. . . . . . .y .> .(-2/5)x - 2

Since the inequality is >, shade the region above the line.
. . (If it was <, shade below the line.)

The graph should look like this:
Code:

```      ::::::::::::::::|::::::::::::::::::       ::::::::::::::::|::::::::::::::::::       o:::::::::::::::|::::::::::::::::::     - - - o:-:-:-:-:-:+:-:-:-:-:-:-:-:-:- -         -5  o:::::::|::::::::::::::::                   o:::|::::::::::::::                     -2o::::::::::::                       |  o::::::```

** With the equation: .2x + 5y .= .-10, the intercepts are easily found.

I perform what I call "Thumb Algebra".

To find the x-intercept, let y = 0.
. . Cover 5y with your thumb and solve: .2x = -10 . . x = -5

To find the y-intercept, let x = 0.
. . Cover 2x with your thumb and solve: .5y = -10 . . y = -2

Got it?