document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885242>Question 885242</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Indicate in standard form the equation of the line passing through the given points.\r<BR>\n" );
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document.write( "G(4, 6), H(1, 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535011 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=535011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the standard form of a line you need a point and then the slope of the line.  We have two points given so we're set there so now we just need to find the slope between those points.   The equation for slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now we can just plug in and find the slope:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%285-6%29%2F%281-4%29 ALIGN=MIDDLE  ALT=\"m=%285-6%29%2F%281-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F-3 ALIGN=MIDDLE  ALT=\"m=-1%2F-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F3%29%29%29%3Cbr%3E%0D%0A%0D%0ASo+the+slope+is+1%2F3.++Now+we+can+pick+a+point+to+work+with.++I+will+work+with+poing+G%284%2C6%29.++There+are+two+ways+that+we+can+finish+this+problem.++We+can+either+1%29+Use+the+Point+Slope+Formula+or+2%29+Solve+y=mx%2Bb+for+b.++I+will+do+both+below.%3Cbr%3E%0D%0A%0D%0A%3Cu%3E1%29Using+Point+Slope+Formula%3C%2Fu%3E%0D%0AThe+point+slope+formula+is+%7B%7B%7By-y1=m%28x-x1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where x1 and y1 are a point on <BR>\n" );
document.write( "the line(in your case (4,6) and m is the slope of the line.  Now we can just plug and chug:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1=m%28x-x1%29 ALIGN=MIDDLE  ALT=\"y-y1=m%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Plug in your point and the slope<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%281%2F3%29%2A%28x-4%29 ALIGN=MIDDLE  ALT=\"y-6=%281%2F3%29%2A%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distribute the 1/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%281%2F3%29%2Ax-4%2F3 ALIGN=MIDDLE  ALT=\"y-6=%281%2F3%29%2Ax-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 6 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax-4%2F3+%2B+6 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-4%2F3+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Get a common denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax-4%2F3+%2B+18%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-4%2F3+%2B+18%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax%2B14%2F3+ ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax%2B14%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Now we can put our answer in standard form.  To do so we need to write it in the form of Ax+By=C.  Which means we need to get x on the other side of the equation and clear the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax%2B14%2F3+ ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax%2B14%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply both sides of the equation by 3 to clear the fractions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=x%2B14+ ALIGN=MIDDLE  ALT=\"3y=x%2B14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > subtract x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B3y=14 ALIGN=MIDDLE  ALT=\"-x%2B3y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<u>2)Solving y=mx+b for b</u><BR>\n" );
document.write( "The other way this can be solved is plugging in the point and the slope into <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;\" > and solving for b.  Remember the slope is 1/3 and the point we are using is (4,6).<br>\r<BR>\n" );
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document.write( "<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;\" >Plug in the slope and the point into the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=1%2F3%284%29%2Bb ALIGN=MIDDLE  ALT=\"6=1%2F3%284%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=4%2F3%2Bb ALIGN=MIDDLE  ALT=\"6=4%2F3%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4/3 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F3+=+b ALIGN=MIDDLE  ALT=\"14%2F3+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Now we now that b = 14/3 so we can plug that into our y=mx+b formula and get y=1/3x+14/3.  Putting that in standard form as we did above you will see that you get the same answer. </SPAN>\n" );
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