document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114944>Question 114944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 14x + 18y = 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83617 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=83617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
document.write( "\n" );
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><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2Ax%2B18%2Ay=10 ALIGN=MIDDLE  ALT=\"14%2Ax%2B18%2Ay=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given equation<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Ay=10-14%2Ax ALIGN=MIDDLE  ALT=\"18%2Ay=10-14%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2Ax ALIGN=MIDDLE  ALT=\"14%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F18%29%2810-14%2Ax%29 ALIGN=MIDDLE  ALT=\"y=%281%2F18%29%2810-14%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F18 ALIGN=MIDDLE  ALT=\"1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F18%29%2810%29-%281%2F18%29%2814%29x%29 ALIGN=MIDDLE  ALT=\"y=%281%2F18%29%2810%29-%281%2F18%29%2814%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F18 ALIGN=MIDDLE  ALT=\"1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10%2F18-%2814%2F18%29x ALIGN=MIDDLE  ALT=\"y=10%2F18-%2814%2F18%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-14%2F18%29%2Ax%2B10%2F18 ALIGN=MIDDLE  ALT=\"y=%28-14%2F18%29%2Ax%2B10%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-7%2F9%29%2Ax%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=%28-7%2F9%29%2Ax%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the equation is now 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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-7%2F9 ALIGN=MIDDLE  ALT=\"m=-7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the slope) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2F9 ALIGN=MIDDLE  ALT=\"b=5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the y-intercept)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So to graph this equation lets plug in some points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=-7<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-7%2F9%29%2A%28-7%29%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=%28-7%2F9%29%2A%28-7%29%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=49%2F9%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=49%2F9%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=54%2F9 ALIGN=MIDDLE  ALT=\"y=54%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's one point (-7,6)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-17%2C12%2C+-11%2C+16%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-7%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-7%2C6%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets find another point <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-7%2F9%29%2A%282%29%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=%28-7%2F9%29%2A%282%29%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-14%2F9%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=-14%2F9%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-9%2F9 ALIGN=MIDDLE  ALT=\"y=-9%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's another point (2,-1). Add this to our graph<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-17%2C12%2C+-11%2C+16%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+2%2C-1%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C-1%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-7%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-7%2C6%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now draw a line through these points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-17%2C12%2C+-11%2C+16%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-17-10%2C-0.777777777777778%2A%28-17-10%29%2B0.555555555555556%2C12%2B10%2C-0.777777777777778%2A%2812%2B10%29%2B0.555555555555556%29%2C%0D%0A++++blue%28+circle%28+2%2C-1%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C-1%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-7%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-7%2C6%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=%28-7%2F9%29%2Ax%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=%28-7%2F9%29%2Ax%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-7,6) and (2,-1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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=-7%2F9 ALIGN=MIDDLE  ALT=\"-7%2F9\"   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  down -7 units and to the right 9 units to get to the next point), the y-intercept is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.555555555555556 ALIGN=MIDDLE  ALT=\"0.555555555555556\"   DISABLED_style= \"max-width:90%; height:auto;\" >) ,or (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F9 ALIGN=MIDDLE  ALT=\"5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.714285714285714 ALIGN=MIDDLE  ALT=\"0.714285714285714\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F7 ALIGN=MIDDLE  ALT=\"5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) . So all of this information verifies our graph.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  We could graph this equation another way. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2F9 ALIGN=MIDDLE  ALT=\"b=5%2F9\"   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=5%2F9 ALIGN=MIDDLE  ALT=\"5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F9 ALIGN=MIDDLE  ALT=\"5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C19%2C+-16.4444444444444%2C+10.5555555555556%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F9 ALIGN=MIDDLE  ALT=\"-7%2F9\"   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=5%2F9 ALIGN=MIDDLE  ALT=\"5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go down 7 units <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C19%2C+-16.4444444444444%2C+10.5555555555556%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+0.555555555555556%2B%28-7%2F2%29%2C+2%2C+-7%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 9 units to get to our next point<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C19%2C+-16.4444444444444%2C+10.5555555555556%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+9%2C-6.44444444444444%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+9%2C-6.44444444444444%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+0.555555555555556%2B%28-7%2F2%29%2C+2%2C+-7%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%289%2F2%29%2C+-6.44444444444444%2C+9%2C+2%2C+0%2C+180+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <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=%28-7%2F9%29%2Ax%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=%28-7%2F9%29%2Ax%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C19%2C+-16.4444444444444%2C+10.5555555555556%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-0.777777777777778%2A%28-10-10%29%2B0.555555555555556%2C19%2B10%2C-0.777777777777778%2A%2819%2B10%29%2B0.555555555555556%29%2C%0D%0A++++blue%28+circle%28+9%2C-6.44444444444444%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+9%2C-6.44444444444444%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0.555555555555556%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+0.555555555555556%2B%28-7%2F2%29%2C+2%2C+-7%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%289%2F2%29%2C+-6.44444444444444%2C+9%2C+2%2C+0%2C+180+%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=%28-7%2F9%29%2Ax%2B5%2F9 ALIGN=MIDDLE  ALT=\"y=%28-7%2F9%29%2Ax%2B5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,0.555555555555556) and (9,-6.44444444444444)<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );