document.write( "Question 143858: graph each system of inequalities
\n" ); document.write( "1. y > -1/2x + 3
\n" ); document.write( " y =< 2/3x -2\r
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\n" ); document.write( "\n" ); document.write( "2. y> 4x
\n" ); document.write( " y =<-5/2x + 4\r
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Algebra.Com's Answer #108315 by mangopeeler07(462) $\"\"$ $\"About$

You can put this solution on YOUR website!
Graph the lines, like so:
\n" ); document.write( " $\"y%3E%28-1%2F2%29x+%2B+3\"$ \r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation $\"1+x+%2B+2+y+=+6\"$ describes a sloping line. For any
\n" ); document.write( " 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.

$\"graph%28+500%2C+500%2C+6-8%2C+6%2B8%2C+3-8%2C+3%2B8%2C+-0.5%2Ax%2B3+%29+\"$ \n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( " $\"y%3C=%282%2F3%29x-2\"$ \r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation $\"-2+x+%2B+3+y+=+-6\"$ describes a sloping line. For any
\n" ); document.write( " 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.

$\"graph%28+500%2C+500%2C+3-8%2C+3%2B8%2C+-2-8%2C+-2%2B8%2C+0.666666666666667%2Ax%2B-2+%29+\"$ \n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( " $\"y%3E4x\"$ \r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation $\"-4+x+%2B+1+y+=+0\"$ describes a sloping line. For any
\n" ); document.write( " 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.

$\"graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+4%2Ax%2B0+%29+\"$ \n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y%3C=%28-5%2F2%29x%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation $\"5+x+%2B+2+y+=+8\"$ describes a sloping line. For any
\n" ); document.write( " 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.

$\"graph%28+500%2C+500%2C+1.6-8%2C+1.6%2B8%2C+4-8%2C+4%2B8%2C+-2.5%2Ax%2B4+%29+\"$ \n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "If you are still in need of assistance grasping this concept, go to my lesson:
\n" ); document.write( "http://www.algebra.com/algebra/homework/Graphs/Inequalities-Made-Easy.lesson \n" ); document.write( "

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