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

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- October 11th 2006, 12:51 AMrobpezliner 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 - October 11th 2006, 01:19 AMCaptainBlack
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 - October 11th 2006, 06:52 AMSoroban
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?