document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67258>Question 67258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> WRITE THE EQUATION of the line passing throiugh the given points:<BR>\n" );
document.write( "(-1, 3)and (4, -2)<BR>\n" );
document.write( "(2, -3) and (2,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47819 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=47819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WRITE THE EQUATION of the line passing throiugh the given points:<BR>\n" );
document.write( "(-1, 3)and (4, -2)<BR>\n" );
document.write( "In order to write the equation of a line, you need a slope and a point.  <BR>\n" );
document.write( "We have two points, therefore we can use the slope formula to find the slope:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m=%28y2-y1%29%2F%28x2-x1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28m=%28y2-y1%29%2F%28x2-x1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, m=slope, and (x1,y1) and (x2,y2) are given points.<BR>\n" );
document.write( "(x1,y1)=(-1,3) and (x2,y2)=(4,-2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-2-3%29%2F%284-%28-1%29%29 ALIGN=MIDDLE  ALT=\"m=%28-2-3%29%2F%284-%28-1%29%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=-5%2F5 ALIGN=MIDDLE  ALT=\"m=-5%2F5\"   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 ALIGN=MIDDLE  ALT=\"m=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that we have a slope and a point we can use the point slope formula to find the equation of the line:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y-y1=m%28x-x1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y-y1=m%28x-x1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, m=slope and (x1,y1) is a given point.<BR>\n" );
document.write( "m=-1 and (x1,y1)=(-1,3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=-1%28x-%28-1%29%29 ALIGN=MIDDLE  ALT=\"y-3=-1%28x-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=-1%28x%2B1%29 ALIGN=MIDDLE  ALT=\"y-3=-1%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=-x-1 ALIGN=MIDDLE  ALT=\"y-3=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3%2B3=-x-1%2B3 ALIGN=MIDDLE  ALT=\"y-3%2B3=-x-1%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-x%2B2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is not the only way to do this, let me know if your book is doing something a little different.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(2, -3) and (2,4)<BR>\n" );
document.write( "This is a special case, notice that the two x's are the same.  If you were to plot these two points and connect the points, you would find you had a vertical line going through x=2.  <BR>\n" );
document.write( "The equation of a vertical line going through x=2, is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "FYI, The other special case would be if the y's were the same, then the equation would be y=k, where k is their matching y value. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Happy Calculating!!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );