document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69071>Question 69071</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618044302/algebrahomeworkh>Algebra  Stucture and Method  Book 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A line passes through (-2,3), (2,5), and (6,k). Find k. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49151 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=49151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start by finding the slope through the points (-2,3), (2,5). You can use the formula: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is simply a formal way to represent \"rise\" over \"run\". By plugging the points (-2,3), (2,5) into the formula it becomes <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-3%29%2F%282-%28-2%29%29 ALIGN=MIDDLE  ALT=\"%285-3%29%2F%282-%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4=1%2F2 ALIGN=MIDDLE  ALT=\"2%2F4=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This number represents the slope of the line running through the points (-2,3), (2,5), and (6,k). To complete the equation of the line, we need to plug in one of those points. For instance, we can use the general form of the line equation: y=mx+b, where m is the slope and b is the y-intercept, and solve for b. So lets plug in the point (-2,3) in the equation along with the given slope:<BR>\n" );
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;\" > using (-2,3) and m=1/2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=%281%2F2%29%28-2%29%2Bb ALIGN=MIDDLE  ALT=\"3=%281%2F2%29%28-2%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > solve for b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=-1%2Bb ALIGN=MIDDLE  ALT=\"3=-1%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > isolate b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=b ALIGN=MIDDLE  ALT=\"4=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so the equation of the line is y=1/2x+4<BR>\n" );
document.write( "Now all we need to do is plug in the point (6,k) to find k. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29%286%29%2B4 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29%286%29%2B4\"   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%2B4 ALIGN=MIDDLE  ALT=\"y=3%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" ><BR>\n" );
document.write( "so k=7 and the point is (6,7) </SPAN>\n" );
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