document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121222>Question 121222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph<BR>\n" );
document.write( "y=-1/3x+1<BR>\n" );
document.write( "y=1/3x+1<BR>\n" );
document.write( "y=-3x+1<BR>\n" );
document.write( "y=3x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88953 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=88953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first two to help you get started\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%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%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%2F3 ALIGN=MIDDLE  ALT=\"m=-1%2F3\"   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%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   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%2F3 ALIGN=MIDDLE  ALT=\"rise%2Frun=-1%2F3\"   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 3. This means that to go from point to point, we can go down 1  and over 3\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 down 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%28-1%2F2%29%2C2%2C-1%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 3 units to get to the next point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,0\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%283%2C0%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%283%2C0%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%28-1%2F2%29%2C2%2C-1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%283%2F2%29%2C0%2C3%2C2%2C+0%2C180%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%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%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%2F3%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%283%2C0%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%283%2C0%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%28-1%2F2%29%2C2%2C-1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%283%2F2%29%2C0%2C3%2C2%2C+0%2C180%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%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%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(3,0\right)\">\r<BR>\n" );
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document.write( "#2\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%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%281%2F3%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%2F3 ALIGN=MIDDLE  ALT=\"m=1%2F3\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=rise%2Frun ALIGN=MIDDLE  ALT=\"slope=rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   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%2F3 ALIGN=MIDDLE  ALT=\"rise%2Frun=1%2F3\"   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 3. This means that to go from point to point, we can go up 1  and over 3\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 3 units to get to the next point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,2\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%283%2C2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%283%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%283%2F2%29%2C2%2C3%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%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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