document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212783>Question 212783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> GRAPH THE EQUATION   y = 1/2x + 3/2\r<BR>\n" );
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document.write( "2)  y = x + 2<BR>\n" );
document.write( "    x + 2y = 16   x= __________   y=_______\r<BR>\n" );
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document.write( "3)  2x = 5y - 3<BR>\n" );
document.write( "    6x - 15y = -3\r<BR>\n" );
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document.write( "4) 5X - 2Y = 36<BR>\n" );
document.write( "   3X + 4Y = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160713 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> GRAPH THE EQUATION y = 1/2x + 3/2<BR>\n" );
document.write( "2) y = x + 2<BR>\n" );
document.write( "x + 2y = 16 x= __________ y=_______<BR>\n" );
document.write( "3) 2x = 5y - 3<BR>\n" );
document.write( "6x - 15y = -3<BR>\n" );
document.write( "4) 5X - 2Y = 36<BR>\n" );
document.write( "3X + 4Y = 6\r<BR>\n" );
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document.write( "Since I didn't understand what you wrote, I answered some of the problems as best as I can in what you meant.\r<BR>\n" );
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document.write( "Step 1.  Just a quick note.  When you have an equation just plot two points x=0 and find y using the equation and x=0 and find x using the equation.   Then draw a line between two point. \r<BR>\n" );
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document.write( "Graph  y = 1/2x + 3/2\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5+x+%2B+1+y+=+1.5 ALIGN=MIDDLE  ALT=\"-0.5+x+%2B+1+y+=+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+--0.5%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--0.5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 1.5/-0.5 = -3.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 1.5/1 = 1.5.</LI><LI>Slope is --0.5/1 = 0.5.</LI><LI> Equation in slope-intercept form: y=0.5*x+1.5.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+1.5-8%2C+1.5%2B8%2C+0.5%2Ax%2B1.5+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+1.5-8%2C+1.5%2B8%2C+0.5%2Ax%2B1.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "Step 2.  The following will solve  y = x + 2\r<BR>\n" );
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document.write( "x + 2y = 16 x= __________ y=_______.  Rewrite y=x+2 as -x+y=2\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+2%5Cy+=+16+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+2%5Cy+=+16+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Ax+=+2+-+1%2Ay ALIGN=MIDDLE  ALT=\"-1%2Ax+=+2+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F-1+-+1%2Ay%2F-1 ALIGN=MIDDLE  ALT=\"x+=+2%2F-1+-+1%2Ay%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A%282%2F-1+-+1%2Ay%2F-1%29+%2B+2%5Cy+=+16 ALIGN=MIDDLE  ALT=\"1%2A%282%2F-1+-+1%2Ay%2F-1%29+%2B+2%5Cy+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=6. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F-1+-+1%2Ay%2F-1 ALIGN=MIDDLE  ALT=\"x+=+2%2F-1+-+1%2Ay%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=4.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=4%2C+y=6+%29 ALIGN=MIDDLE  ALT=\"system%28+x=4%2C+y=6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Step 3.  The following will solve  3) 2x = 5y - 3, 6x - 15y = -3\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++-2%5Cx+%2B+5%5Cy+=+3%2C%0D%0A++++6%5Cx+%2B+-15%5Cy+=+-3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++-2%5Cx+%2B+5%5Cy+=+3%2C%0D%0A++++6%5Cx+%2B+-15%5Cy+=+-3+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 5*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Ax+=+3+-+5%2Ay ALIGN=MIDDLE  ALT=\"-2%2Ax+=+3+-+5%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F-2+-+5%2Ay%2F-2 ALIGN=MIDDLE  ALT=\"x+=+3%2F-2+-+5%2Ay%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%283%2F-2+-+5%2Ay%2F-2%29+%2B+-15%5Cy+=+-3 ALIGN=MIDDLE  ALT=\"6%2A%283%2F-2+-+5%2Ay%2F-2%29+%2B+-15%5Cy+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=-6=0. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F-2+-+5%2Ay%2F-2 ALIGN=MIDDLE  ALT=\"x+=+3%2F-2+-+5%2Ay%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=-16.5.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-16.5%2C+y=-6=0+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-16.5%2C+y=-6=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Step 4.  The following will solve 5X - 2Y = 36,  3X + 4Y = 6\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++5%5Cx+%2B+-2%5Cy+=+36%2C%0D%0A++++3%5Cx+%2B+4%5Cy+=+6+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++5%5Cx+%2B+-2%5Cy+=+36%2C%0D%0A++++3%5Cx+%2B+4%5Cy+=+6+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving -2*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax+=+36+-+-2%2Ay ALIGN=MIDDLE  ALT=\"5%2Ax+=+36+-+-2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+36%2F5+-+-2%2Ay%2F5 ALIGN=MIDDLE  ALT=\"x+=+36%2F5+-+-2%2Ay%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%2836%2F5+-+-2%2Ay%2F5%29+%2B+4%5Cy+=+6 ALIGN=MIDDLE  ALT=\"3%2A%2836%2F5+-+-2%2Ay%2F5%29+%2B+4%5Cy+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=-3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+36%2F5+-+-2%2Ay%2F5 ALIGN=MIDDLE  ALT=\"x+=+36%2F5+-+-2%2Ay%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=6.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=6%2C+y=-3+%29 ALIGN=MIDDLE  ALT=\"system%28+x=6%2C+y=-3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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