SOLUTION: graph each system of inequalities 1. y > -1/2x + 3 y =< 2/3x -2 2. y> 4x y =<-5/2x + 4

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Question 143858: graph each system of inequalities
1. y > -1/2x + 3
y =< 2/3x -2

2. y> 4x
y =<-5/2x + 4

Answer by mangopeeler07(462)   (Show Source): You can put this solution on YOUR website!
Graph the lines, like so:

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/1 = 6.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/2 = 3.
  • Slope is -1/2 = -0.5.
  • Equation in slope-intercept form: y=-0.5*x+3.



Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -6/-2 = 3.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -6/3 = -2.
  • Slope is --2/3 = 0.666666666666667.
  • Equation in slope-intercept form: y=0.666666666666667*x+-2.



Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/-4 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/1 = 0.
  • Slope is --4/1 = 4.
  • Equation in slope-intercept form: y=4*x+0.



Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/5 = 1.6.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -5/2 = -2.5.
  • Equation in slope-intercept form: y=-2.5*x+4.


Once you have graphed them, for and , dot the line and shade above it. For and , shade below the line.
If you are still in need of assistance grasping this concept, go to my lesson:
http://www.algebra.com/algebra/homework/Graphs/Inequalities-Made-Easy.lesson
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