document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90275>Question 90275</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph f(x) = 4x + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65514 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=65514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\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=graphing_linear_equations.solver>Graphing Linear Equations</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=4%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we only need to plug in two points to draw the line<BR>\n" );
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document.write( "  So lets plug in some points<BR>\n" );
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document.write( "  Plug in x=-2<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2A%28-2%29%2B1 ALIGN=MIDDLE  ALT=\"y=4%2A%28-2%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8%2B1 ALIGN=MIDDLE  ALT=\"y=-8%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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document.write( "  So here's one point (-2,-7)<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+-12%2C9%2C+-17%2C+7%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now lets find another point <BR>\n" );
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document.write( "  Plug in x=-1<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2A%28-1%29%2B1 ALIGN=MIDDLE  ALT=\"y=4%2A%28-1%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%2B1 ALIGN=MIDDLE  ALT=\"y=-4%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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document.write( "  So here's another point (-1,-3). Add this to our graph<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+-12%2C9%2C+-17%2C+7%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-1%2C-3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now draw a line through these points<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+-12%2C9%2C+-17%2C+7%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-12-10%2C4%2A%28-12-10%29%2B1%2C9%2B10%2C4%2A%289%2B10%29%2B1%29%2C%0D%0A++++blue%28+circle%28+-1%2C-3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.1%2C+1.5+%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=4%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=4%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-2,-7) and (-1,-3)<BR>\n" );
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document.write( "  So from the graph we can see that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F1 ALIGN=MIDDLE  ALT=\"4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which tells us that in order to go from point to point we have to start at one point and go  up 4 units and to the right 1 units to get to the next point) the y-intercept is (0,<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 the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.25 ALIGN=MIDDLE  ALT=\"-0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) <BR>\n" );
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document.write( "  We could graph this equation another way. 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 (the point where the graph intersects with the y-axis) is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
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document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<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%2C11%2C+-9%2C+15%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14-0.05%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F1 ALIGN=MIDDLE  ALT=\"4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that in order to go from point to point we can use the slope to do so. So starting at (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go up 4 units <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%2C11%2C+-9%2C+15%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+1%2B%284%2F2%29%2C+2%2C+4%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  and to the right 1 units to get to our next point<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%2C11%2C+-9%2C+15%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+1%2C5%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C5%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+1%2B%284%2F2%29%2C+2%2C+4%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+5%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Now draw a line through those points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=4%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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%2C11%2C+-9%2C+15%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C4%2A%28-10-10%29%2B1%2C11%2B10%2C4%2A%2811%2B10%29%2B1%29%2C%0D%0A++++blue%28+circle%28+1%2C5%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C5%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+1%2B%284%2F2%29%2C+2%2C+4%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+5%2C+1%2C+2%2C+180%2C+360+%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=4%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=4%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,1) and (1,5)<BR>\n" );
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