document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129697>Question 129697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the slope intercept form of an equation that passes throught (8, -2) and is perpendicular to the graph 5x-3y=7. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94686 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=94686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "First convert the standard equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-3y=7 ALIGN=MIDDLE  ALT=\"5x-3y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope intercept form\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=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-3y=7 ALIGN=MIDDLE  ALT=\"5x-3y=7\"   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-3y-5x=7-5x ALIGN=MIDDLE  ALT=\"5x-3y-5x=7-5x\"   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%2B7 ALIGN=MIDDLE  ALT=\"-3y=-5x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3y%29%2F%28-3%29=%28-5x%2B7%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"%28-3y%29%2F%28-3%29=%28-5x%2B7%29%2F%28-3%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%28-3%29%2B%287%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y+=+%28-5x%29%2F%28-3%29%2B%287%29%2F%28-3%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+=+%285%2F3%29x-7%2F3 ALIGN=MIDDLE  ALT=\"y+=+%285%2F3%29x-7%2F3\"   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-3y=7 ALIGN=MIDDLE  ALT=\"5x-3y=7\"   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+=+%285%2F3%29x-7%2F3 ALIGN=MIDDLE  ALT=\"y+=+%285%2F3%29x-7%2F3\"   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+=+%285%2F3%29x-7%2F3 ALIGN=MIDDLE  ALT=\"y+=+%285%2F3%29x-7%2F3\"   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=-7%2F3 ALIGN=MIDDLE  ALT=\"b=-7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "Now let's find the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F3%29x-7%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F3%29x-7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through (8,-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=equation_parallel_or_perpendicular.solver>Finding the Equation of a Line Parallel or Perpendicular to a Given Line</A></TD></TR>\n" );
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document.write( "  Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of <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;\" >, you can find the perpendicular slope by this formula:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2Fm ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D ALIGN=MIDDLE  ALT=\"m%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2F%285%2F3%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%285%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So plug in the given slope to find the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=%28-1%2F1%29%283%2F5%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > When you divide fractions, you multiply the first fraction (which is really <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) by the reciprocal of the second<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-3%2F5 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fractions.<BR>\n" );
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document.write( "  So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So now we know the slope of the unknown line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its the negative reciprocal of  <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;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F3%29%2Ax-7%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F3%29%2Ax-7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (8,-2), we can find the equation by plugging in this info into the point-slope formula<BR>\n" );
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document.write( "  Point-Slope Formula:<BR>\n" );
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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" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=%28-3%2F5%29%2A%28x-8%29 ALIGN=MIDDLE  ALT=\"y%2B2=%28-3%2F5%29%2A%28x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F5 ALIGN=MIDDLE  ALT=\"m=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=8 ALIGN=MIDDLE  ALT=\"x%5B1%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-2 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=%28-3%2F5%29%2Ax%2B%283%2F5%29%288%29 ALIGN=MIDDLE  ALT=\"y%2B2=%28-3%2F5%29%2Ax%2B%283%2F5%29%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=%28-3%2F5%29%2Ax%2B24%2F5 ALIGN=MIDDLE  ALT=\"y%2B2=%28-3%2F5%29%2Ax%2B24%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F5%29%2Ax%2B24%2F5-2 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B24%2F5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides to isolate y<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F5%29%2Ax%2B24%2F5-10%2F5 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B24%2F5-10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make into equivalent fractions with equal denominators<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F5%29%2Ax%2B14%2F5 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F5%29%2Ax%2B14%2F5 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
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document.write( "   So the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F3%29%2Ax-7%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F3%29%2Ax-7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F5%29%2Ax%2B14%2F5 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So here are the graphs of the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F3%29%2Ax-7%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F3%29%2Ax-7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F5%29%2Ax%2B14%2F5 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-5%2C13%2C-12%2C3%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C13%2C-12%2C3%2C+1.66666666666667%2Ax%2B-7%2F3%2C+-0.6%2Ax%2B2.8%29%2C%0D%0A+++++++++++circle%288%2C-2%2C0.05%29%2C%0D%0A+++++++++++circle%288%2C-2%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=%285%2F3%29%2Ax-7%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F3%29%2Ax-7%2F3\"   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=%28-3%2F5%29%2Ax%2B14%2F5 ALIGN=MIDDLE  ALT=\"y=%28-3%2F5%29%2Ax%2B14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green) that is perpendicular to the given graph and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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