document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403352>Question 403352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the equation of the line passing through the point (1,1) and parallel to y=5x-6?\r<BR>\n" );
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document.write( "I am having a very tough time figuring this problem, any help is greatly appreciated! Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285228 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=285228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember that <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;\" > is the slope-intercept form of an equation where <BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-6 ALIGN=MIDDLE  ALT=\"y=5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5 ALIGN=MIDDLE  ALT=\"m=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which means that the slope is 5.\r<BR>\n" );
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document.write( "Also, remember that any two parallel lines have the same slope. So the slope of the unknown parallel line is 5 (since it's parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-6 ALIGN=MIDDLE  ALT=\"y=5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which has a slope of 5)\r<BR>\n" );
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document.write( "So we now know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5 ALIGN=MIDDLE  ALT=\"m=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for this unknown line.\r<BR>\n" );
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document.write( "Go back to <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;\" > and plug it in to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%2Bb ALIGN=MIDDLE  ALT=\"y=5x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we're forcing this new unknown line to go through (1,1). So when x=1, y=1. Plug these values in to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=5%281%29%2Bb ALIGN=MIDDLE  ALT=\"1=5%281%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and solve for b to get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=5%281%29%2Bb ALIGN=MIDDLE  ALT=\"1=5%281%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=5%2Bb ALIGN=MIDDLE  ALT=\"1=5%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-5=b ALIGN=MIDDLE  ALT=\"1-5=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=b ALIGN=MIDDLE  ALT=\"-4=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the last piece of the puzzle. So the y-intercept of this unknown line is (0,-4) because all y-intercepts are of the form (0, some number)\r<BR>\n" );
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document.write( "So in summary, we know that the unknown (soon not really unknown) line has a slope of 5, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5 ALIGN=MIDDLE  ALT=\"m=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is (0,-4) making <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So plug all of this new info into <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;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-4 ALIGN=MIDDLE  ALT=\"y=5x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the equation of the parallel line to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-6 ALIGN=MIDDLE  ALT=\"y=5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  that goes through (1,1) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-4 ALIGN=MIDDLE  ALT=\"y=5x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "------------------------------------------------------------------------\r<BR>\n" );
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document.write( "<font color=red>Answer</font>\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-4 ALIGN=MIDDLE  ALT=\"y=5x-4\"   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=%0D%0Adrawing%28+500%2C+500%2C+-10%2C10%2C+-10%2C+10%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C10%2C+-10%2C+10%2C5x-6%2C5x-4%29%2C%0D%0Acircle%281%2C1%2C0.03%29%2Ccircle%281%2C1%2C0.05%29%2Ccircle%281%2C1%2C0.08%29%2Ccircle%281%2C1%2C0.1%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how the green line (the previously unknown equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-4 ALIGN=MIDDLE  ALT=\"y=5x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is parallel to the given red line (the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-6 ALIGN=MIDDLE  ALT=\"y=5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the green line goes through (1,1). So we've shown that our answer is correct. </SPAN>\n" );
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