robpez!
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?