document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118013>Question 118013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of each line. Give the answer in standard form using only integers as the coefficients.\r<BR>\n" );
document.write( "\n" );
document.write( "The line through (3,4) that is parallel to the line 5x+3y=9\r<BR>\n" );
document.write( "\n" );
document.write( "The answer is 5x+3y=27\r<BR>\n" );
document.write( "\n" );
document.write( "How do I work the problem to get the above answer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86055 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First convert 5x+3y=9 into slope-intercept form\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y=9 ALIGN=MIDDLE  ALT=\"5x%2B3y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y-5x=9-5x ALIGN=MIDDLE  ALT=\"5x%2B3y-5x=9-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 5x from both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-5x%2B9 ALIGN=MIDDLE  ALT=\"3y=-5x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283y%29%2F%283%29=%28-5x%2B9%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%283y%29%2F%283%29=%28-5x%2B9%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate y<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5x%29%2F%283%29%2B%289%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5x%29%2F%283%29%2B%289%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the right hand side<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5%2F3%29x%2B3 ALIGN=MIDDLE  ALT=\"y+=+%28-5%2F3%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y=9 ALIGN=MIDDLE  ALT=\"5x%2B3y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5%2F3%29x%2B3 ALIGN=MIDDLE  ALT=\"y+=+%28-5%2F3%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5%2F3%29x%2B3 ALIGN=MIDDLE  ALT=\"y+=+%28-5%2F3%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F3 ALIGN=MIDDLE  ALT=\"m=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's find the equation of the line through (3,4) that is parallel to the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29x%2B3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=equation_parallel_or_perpendicular.solver>Finding the Equation of a Line Parallel or Perpendicular to a Given Line</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since any two parallel lines have the same slope we know the slope of the unknown line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F3 ALIGN=MIDDLE  ALT=\"-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its from the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F3 ALIGN=MIDDLE  ALT=\"-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (3,4), we can find the equation by plugging in this info into the point-slope formula<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Point-Slope Formula:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where m is the slope and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is the given point<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=%28-5%2F3%29%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"y-4=%28-5%2F3%29%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F3 ALIGN=MIDDLE  ALT=\"m=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=4 ALIGN=MIDDLE  ALT=\"y%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=%28-5%2F3%29%2Ax%2B%285%2F3%29%283%29 ALIGN=MIDDLE  ALT=\"y-4=%28-5%2F3%29%2Ax%2B%285%2F3%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F3 ALIGN=MIDDLE  ALT=\"-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=%28-5%2F3%29%2Ax%2B15%2F3 ALIGN=MIDDLE  ALT=\"y-4=%28-5%2F3%29%2Ax%2B15%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B15%2F3%2B4 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B15%2F3%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B15%2F3%2B12%2F3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B15%2F3%2B12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make into equivalent fractions with equal denominators<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B27%2F3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B27%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
document.write( "  <BR>\n" );
document.write( "   So the equation of the line that is parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here are the graphs of the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-5%2C8%2C-2%2C9%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C8%2C-2%2C9%2C+-1.66666666666667%2Ax%2B3%2C+-1.66666666666667%2Ax%2B9%29%2C%0D%0A+++++++++++circle%283%2C4%2C0.05%29%2C%0D%0A+++++++++++circle%283%2C4%2C0.08%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and graph of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green) that is parallel to the given graph and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29x%2B9 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to standard form\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5%2F3%29x%2B9 ALIGN=MIDDLE  ALT=\"y+=+%28-5%2F3%29x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ay+=+3%2A%28%28-5%2F3%29x%2B9%29 ALIGN=MIDDLE  ALT=\"3%2Ay+=+3%2A%28%28-5%2F3%29x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 3<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+-5x%2B27 ALIGN=MIDDLE  ALT=\"3y+=+-5x%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B5x+=+-5x%2B27%2B5x ALIGN=MIDDLE  ALT=\"3y%2B5x+=+-5x%2B27%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5x to both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y+=+27 ALIGN=MIDDLE  ALT=\"5x%2B3y+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-5%2F3%29x%2B9 ALIGN=MIDDLE  ALT=\"y+=+%28-5%2F3%29x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y+=+27 ALIGN=MIDDLE  ALT=\"5x%2B3y+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form where A > 0)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y+=+27 ALIGN=MIDDLE  ALT=\"5x%2B3y+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%2BBy+=+C ALIGN=MIDDLE  ALT=\"Ax%2BBy+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+5 ALIGN=MIDDLE  ALT=\"A+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+3 ALIGN=MIDDLE  ALT=\"B+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+27 ALIGN=MIDDLE  ALT=\"C+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br><br></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y=27 ALIGN=MIDDLE  ALT=\"5x%2B3y=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );