document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948988>Question 948988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph each line<BR>\n" );
document.write( "Slope -1, through 3,5\r<BR>\n" );
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document.write( "Graph each line<BR>\n" );
document.write( "No slope, through (2,-1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579279 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=579279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<BR>\n" );
document.write( "given: graph a line that has<BR>\n" );
document.write( "a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and passes 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=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\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=find_line_by_slope_and_point.solver>FIND a line by slope and one point</A></TD></TR>\n" );
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document.write( "  What we know about the line whose equation we are trying to find out:<BR>\n" );
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document.write( "      <LI>it goes through point (3, 5)</LI><BR>\n" );
document.write( "      <LI>it has a slope of -1</LI><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  First, let's draw a diagram of the coordinate system with point (3, 5) plotted with a little blue dot:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++++drawing%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++++++grid%281%29%2C%0D%0A+++++++++++++blue%28+circle%28+3%2C+5%2C+0.2+%29+%29+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    <B>Write this down</B>: the formula for the equation, given point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2C+y%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D%2C+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and intercept a, is<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see a paragraph below explaining why this formula is correct)<BR>\n" );
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document.write( "    Given that a=-1, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x%5B1%5D+=+3%2C+y%5B1%5D+=+5+%29+ ALIGN=MIDDLE  ALT=\"system%28+x%5B1%5D+=+3%2C+y%5B1%5D+=+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have the equation of the line:<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2Ax+%2B+8 ALIGN=MIDDLE  ALT=\"y=-1%2Ax+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Explanation: <I>Why did we use formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (<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;\" >) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (<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;\" >): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+a%2Ax%5B1%5D%2Bb ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+a%2Ax%5B1%5D%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Here, we know a, <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;\" >, and <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;\" >, and do not know b. It is easy to find out: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, then, the equation of the line is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+ ALIGN=MIDDLE  ALT=\"+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </I><BR>\n" );
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document.write( "    Here's the graph:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++++drawing%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++++++grid%281%29%2C%0D%0A+++++++++++++graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-1%2Ax%2B8+%29%2C%0D%0A+++++++++++++blue%28+circle%28+3%2C+5%2C+0.2+%29+%29%2C%0D%0A+++++++++++++locate%28+3%2C+5%2C+%22%283%2C+5%29%22+%29+%29%0D%0A+++++++++++++%29%0D%0A++++++++++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "Graph each line that has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > slope, through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "vertical lines have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NO ALIGN=MIDDLE  ALT=\"NO\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SLOPE ALIGN=MIDDLE  ALT=\"SLOPE\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it is parallel to y-axis passing through <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   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=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%282%2C-1%2C.12%29%2Clocate%282%2C-1%2Cp%282%2C-1%29%29%2Cline%282%2C10%2C2%2C-10%29%2C+%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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