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

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


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the lines, like so:
y%3E%28-1%2F2%29x+%2B+3
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+2+y+=+6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F2.
  • 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.
graph%28+500%2C+500%2C+6-8%2C+6%2B8%2C+3-8%2C+3%2B8%2C+-0.5%2Ax%2B3+%29+


y%3C=%282%2F3%29x-2
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -2+x+%2B+3+y+=+-6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--2%2F3.
  • 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.
graph%28+500%2C+500%2C+3-8%2C+3%2B8%2C+-2-8%2C+-2%2B8%2C+0.666666666666667%2Ax%2B-2+%29+


y%3E4x
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -4+x+%2B+1+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--4%2F1.
  • 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.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+4%2Ax%2B0+%29+


y%3C=%28-5%2F2%29x%2B4
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 5+x+%2B+2+y+=+8 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-5%2F2.
  • 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.
graph%28+500%2C+500%2C+1.6-8%2C+1.6%2B8%2C+4-8%2C+4%2B8%2C+-2.5%2Ax%2B4+%29+


Once you have graphed them, for y%3E%28-1%2F2%29x+%2B+3 and y%3E4x, dot the line and shade above it. For y%3C=%282%2F3%29x-2 and y%3C=%28-5%2F2%29x%2B4, 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