document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888036>Question 888036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation in slope-intercept form for the line that passes through (3,7) and (7,4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537020 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39629)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=537020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation in slope-intercept form for the line that passes through (h,k) and (u,v).\r<BR>\n" );
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document.write( "Slope-intercept form is <b>y=mx+b</b>, using m for slope and b for y-intercept.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28m=%28v-k%29%2F%28u-h%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28m=%28v-k%29%2F%28u-h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving the basic equation for b,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y-mx ALIGN=MIDDLE  ALT=\"b=y-mx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and picking either given point, here arbitrarily choosing (h,k) you can find b:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=k-mh ALIGN=MIDDLE  ALT=\"b=k-mh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=k-%28%28v-k%29%2F%28u-h%29%29h ALIGN=MIDDLE  ALT=\"b=k-%28%28v-k%29%2F%28u-h%29%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you might like to simplify the expression (or number) b:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%28k%28u-h%29-h%28v-k%29%29%2F%28u-h%29 ALIGN=MIDDLE  ALT=\"b=%28k%28u-h%29-h%28v-k%29%29%2F%28u-h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%28ku-hk-hv%2Bhk%29%2F%28u-h%29 ALIGN=MIDDLE  ALT=\"b=%28ku-hk-hv%2Bhk%29%2F%28u-h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, notice the additive inverses hk and -hk,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28b=%28ku-hv%29%2F%28u-h%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28b=%28ku-hv%29%2F%28u-h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Revising the slope-intercept form generalized equation for the two given points,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%28%28v-k%29%2F%28u-h%29%29x%2B%28ku-hv%29%2F%28u-h%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%28%28v-k%29%2F%28u-h%29%29x%2B%28ku-hv%29%2F%28u-h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that the process may seem less involved when using actual coordinate values; but not always.  At least with this demonstration, nothing is hidden, and this is generalized.   </SPAN>\n" );
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