document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212929>Question 212929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do I find the equation of the line which passes through the points\r<BR>\n" );
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document.write( "   (-1,2) and (-2,0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160880 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do I find the equation of the line which passes through the points\r<BR>\n" );
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document.write( "   (-1,2) and (-2,0)\r<BR>\n" );
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document.write( "However, here are the steps showing you how you can check your work with one of the points.\r<BR>\n" );
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document.write( "Step 1.  The slope of the line m is given as\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;\" >\r<BR>\n" );
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document.write( "where for our example is  (-1,2) and (-2,0)  x1=-1, y1=2, x2=-2 and y2=0 (think of <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;\" >).  You can choose the points the other way around but be consistent with the x and y coordinates.  You will get the same result.\r<BR>\n" );
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document.write( "Step 2.  Substituting the above values in the slope equation gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%280-2%29%2F%28-2-%28-1%29%29 ALIGN=MIDDLE  ALT=\"m=%280-2%29%2F%28-2-%28-1%29%29\"   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=m=-2%2F-1 ALIGN=MIDDLE  ALT=\"m=-2%2F-1\"   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=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  The slope is calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  Now use the slope equation of step 1 and choose one of the given points.  I'll choose point (-1,2).   Letting y=y2 and x=x2 and substituting m=-3 in the slope equation given as,\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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2=%28y-2%29%2F%28x-%28-1%29%29 ALIGN=MIDDLE  ALT=\"+2=%28y-2%29%2F%28x-%28-1%29%29\"   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=2=%28y-2%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"2=%28y-2%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  Multiply both sides of equation by x+1 to get rid of denomination found on the right side of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28x%2B1%29=%28x%2B1%29%28y-2%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"+2%28x%2B1%29=%28x%2B1%29%28y-2%29%2F%28x%2B1%29\"   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=2%28x%2B1%29=y-2 ALIGN=MIDDLE  ALT=\"2%28x%2B1%29=y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Now simplify and put the above equation into slope-intercept form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2=y-2 ALIGN=MIDDLE  ALT=\"2x%2B2=y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 2 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2%2B2=y-2%2B2 ALIGN=MIDDLE  ALT=\"2x%2B2%2B2=y-2%2B2\"   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=2x%2B4=y ALIGN=MIDDLE  ALT=\"2x%2B4=y\"   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=y=2x%2B4 ALIGN=MIDDLE  ALT=\"y=2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ANSWER in slope-intercept form.  m=2 and y-intercept=4\r<BR>\n" );
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document.write( "Step 7.  See if the other point (-2,0) or x=-2 and y=0 satisfies this equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B4 ALIGN=MIDDLE  ALT=\"y=2x%2B4\"   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=0=2%2A%28-2%29%2B4 ALIGN=MIDDLE  ALT=\"0=2%2A%28-2%29%2B4\"   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=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So the point (-2,0) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.\r<BR>\n" );
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document.write( "Note;  above equation can be also be transform into standard form as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By=4 ALIGN=MIDDLE  ALT=\"-2x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See graph below to check the above steps.\r<BR>\n" );
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document.write( "<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=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+x+%2B+1+y+=+4 ALIGN=MIDDLE  ALT=\"-2+x+%2B+1+y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+--2%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 4/-2 = -2.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.</LI><LI>Slope is --2/1 = 2.</LI><LI> Equation in slope-intercept form: y=2*x+4.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+4-8%2C+4%2B8%2C+2%2Ax%2B4+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+4-8%2C+4%2B8%2C+2%2Ax%2B4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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