document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146634>Question 146634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP HELP HELP.....PLEASE PLEASE<BR>\n" );
document.write( "Question 1:  Write equation of the line containing the given point and parallel to the given line y=mx+b:<BR>\n" );
document.write( " A.   (5,7) x + 7y =5   The equation line is y???<BR>\n" );
document.write( " B.   (-9,5)4x =5y + 7  The equation line is y???\r<BR>\n" );
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document.write( "Question 2:  Write equation of a line containing given point and perpendicular to given line.  <BR>\n" );
document.write( "  A.  Express answer y=mx+b (3,6); 8x + y = 9  The equation of the line is y???<BR>\n" );
document.write( "  B.  (2,-6); 8x +3y =3  The equation of the line is y??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107072 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=107072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do one of each to get you started\r<BR>\n" );
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document.write( "A)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+7y+=5 ALIGN=MIDDLE  ALT=\"x+%2B+7y+=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F7%29x%2B5%2F7 ALIGN=MIDDLE  ALT=\"y=-%281%2F7%29x%2B5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for y.\r<BR>\n" );
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document.write( "We can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F7%29x%2B5%2F7 ALIGN=MIDDLE  ALT=\"y=-%281%2F7%29x%2B5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F7 ALIGN=MIDDLE  ALT=\"m=-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2F7 ALIGN=MIDDLE  ALT=\"b=5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F7 ALIGN=MIDDLE  ALT=\"m=-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F7 ALIGN=MIDDLE  ALT=\"m=-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and the coordinates of the given point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(5,7\right\)\">.\r<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;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=%28-1%2F7%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y-7=%28-1%2F7%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F7 ALIGN=MIDDLE  ALT=\"m=-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=5 ALIGN=MIDDLE  ALT=\"x%5B1%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=7 ALIGN=MIDDLE  ALT=\"y%5B1%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=%28-1%2F7%29x%2B%28-1%2F7%29%28-5%29 ALIGN=MIDDLE  ALT=\"y-7=%28-1%2F7%29x%2B%28-1%2F7%29%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=%28-1%2F7%29x%2B5%2F7 ALIGN=MIDDLE  ALT=\"y-7=%28-1%2F7%29x%2B5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F7%29x%2B5%2F7%2B7 ALIGN=MIDDLE  ALT=\"y=%28-1%2F7%29x%2B5%2F7%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 7 to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F7%29x%2B54%2F7 ALIGN=MIDDLE  ALT=\"y=%28-1%2F7%29x%2B54%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. note: If you need help with fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a>.\r<BR>\n" );
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document.write( "So the equation of the line parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+7y+=5 ALIGN=MIDDLE  ALT=\"x+%2B+7y+=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(5,7\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F7%29x%2B54%2F7 ALIGN=MIDDLE  ALT=\"y=%28-1%2F7%29x%2B54%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here's a graph to visually verify our answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F7%29x%2B5%2F7%2C%28-1%2F7%29x%2B54%2F7%29%2C%0D%0Acircle%285%2C7%2C0.08%29%2C%0D%0Acircle%285%2C7%2C0.10%29%2C%0D%0Acircle%285%2C7%2C0.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Graph of the original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F7%29x%2B5%2F7 ALIGN=MIDDLE  ALT=\"y=-%281%2F7%29x%2B5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and the parallel line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F7%29x%2B54%2F7 ALIGN=MIDDLE  ALT=\"y=%28-1%2F7%29x%2B54%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(5,7\right\)\">. \r<BR>\n" );
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document.write( "2)\r<BR>\n" );
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document.write( "A)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+%2B+y+=+9 ALIGN=MIDDLE  ALT=\"8x+%2B+y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=-8%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for y.\r<BR>\n" );
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document.write( "We can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=-8%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-8 ALIGN=MIDDLE  ALT=\"m=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=9 ALIGN=MIDDLE  ALT=\"b=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now to find the slope of the perpendicular line, simply flip the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-8 ALIGN=MIDDLE  ALT=\"m=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F8 ALIGN=MIDDLE  ALT=\"m=-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now change the sign to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F8 ALIGN=MIDDLE  ALT=\"m=1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F8 ALIGN=MIDDLE  ALT=\"m=1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-8 ALIGN=MIDDLE  ALT=\"m=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the coordinates of the given point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(3,6\right\)\">.\r<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;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%281%2F8%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y-6=%281%2F8%29%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=1%2F8 ALIGN=MIDDLE  ALT=\"m=1%2F8\"   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=6 ALIGN=MIDDLE  ALT=\"y%5B1%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%281%2F8%29x%2B%281%2F8%29%28-3%29 ALIGN=MIDDLE  ALT=\"y-6=%281%2F8%29x%2B%281%2F8%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%281%2F8%29x-3%2F8 ALIGN=MIDDLE  ALT=\"y-6=%281%2F8%29x-3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F8%29x-3%2F8%2B6 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29x-3%2F8%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 6 to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F8%29x%2B45%2F8 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29x%2B45%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. note: If you need help with fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a>.\r<BR>\n" );
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document.write( "So the equation of the line perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+%2B+y+=+9 ALIGN=MIDDLE  ALT=\"8x+%2B+y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(3,6\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F8%29x%2B45%2F8 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29x%2B45%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here's a graph to visually verify our answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-8%2Ax%2B9%2C%281%2F8%29x%2B45%2F8%29%0D%0Acircle%283%2C6%2C0.08%29%2C%0D%0Acircle%283%2C6%2C0.10%29%2C%0D%0Acircle%283%2C6%2C0.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Graph of the original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8%2Ax%2B9 ALIGN=MIDDLE  ALT=\"y=-8%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and the perpendicular line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F8%29x%2B45%2F8 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29x%2B45%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(3,6\right\)\">. <BR>\n" );
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