document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253949>Question 253949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a linear equation.\r<BR>\n" );
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document.write( "y = 1/2x + 1\r<BR>\n" );
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document.write( "Part a\r<BR>\n" );
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document.write( "Complete this table of values for the equation.\r<BR>\n" );
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document.write( "                   Input X           Output Y\r<BR>\n" );
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document.write( "                    -4/\r<BR>\n" );
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document.write( "                    -2/\r<BR>\n" );
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document.write( "                     0\r<BR>\n" );
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document.write( "                     2\r<BR>\n" );
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document.write( "                     4\r<BR>\n" );
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document.write( "These are the values that I came up with for the Y output\r<BR>\n" );
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document.write( "                     -4/    -1\r<BR>\n" );
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document.write( "                     -2/     0\r<BR>\n" );
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document.write( "                      0/     1\r<BR>\n" );
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document.write( "                      2/     2\r<BR>\n" );
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document.write( "                      4/     3\r<BR>\n" );
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document.write( "I hope that I have the Y output values correct.  Do I?\r<BR>\n" );
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document.write( "The problem is that I now have to graph the equation which I did complete,<BR>\n" );
document.write( "but I want to make sure that I did it correctly.\r<BR>\n" );
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document.write( "I don't know if anyone can put a graph on here so that I can see if mine is<BR>\n" );
document.write( "correct.\r<BR>\n" );
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document.write( "This is how I plotted the points on my X and Y axis graph.\r<BR>\n" );
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document.write( "I looked at the points and plotted them like this  (-4/-01)<BR>\n" );
document.write( "                                                    (-2/0)<BR>\n" );
document.write( "                                                     (0,1)<BR>\n" );
document.write( "                                                      (2,2)<BR>\n" );
document.write( "                                                       (4,3)\r<BR>\n" );
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document.write( "It ended up looking like the slope of a mountain from the lower left being the<BR>\n" );
document.write( "lowest and gradually increasing as a slope.\r<BR>\n" );
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document.write( "Can you please tell me if my output values are correct, and the way I handled<BR>\n" );
document.write( "graphing the values.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186322 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=186322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the equation is in slope-intercept 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 the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F2 ALIGN=MIDDLE  ALT=\"m=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > this tells us that the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\">.Remember the y-intercept is the point where the graph intersects with the y-axis\r<BR>\n" );
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document.write( "So we have one point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now since the slope is comprised of the \"rise\" over the \"run\" this means\r<BR>\n" );
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document.write( "Also, because the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rise%2Frun=1%2F2 ALIGN=MIDDLE  ALT=\"rise%2Frun=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which shows us that the rise is 1 and the run is 2. This means that to go from point to point, we can go up 1  and over 2\r<BR>\n" );
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document.write( "So starting at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\">, go up 1 unit \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%281%2F2%29%2C2%2C1%2C90%2C270%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and to the right 2 units to get to the next point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(2,2\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%2C%0D%0A++blue%28circle%282%2C2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%282%2C2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%281%2F2%29%2C2%2C1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%282%2F2%29%2C2%2C2%2C2%2C+180%2C360%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now draw a line through these points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B1\"   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%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%281%2F2%29x%2B1%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%2C%0D%0A++blue%28circle%282%2C2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%282%2C2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%281%2F2%29%2C2%2C1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%282%2F2%29%2C2%2C2%2C2%2C+180%2C360%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(2,2\right)\"> </SPAN>\n" );
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