document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204563>Question 1204563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line that passes through the pair of points.\r<BR>\n" );
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document.write( "(−2, −3), (4, 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840888 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The responses from both of the other tutors say to plug numbers into a formula that gives you the equation of a line passing through two given points.<br><BR>\n" );
document.write( "If you are in a job where you have to do that 50 times a day, then having a formula to plug numbers into is useful.<br><BR>\n" );
document.write( "But plugging numbers into a formula doesn't teach you much.  And what if you are a beginning student and are not familiar with the formula and accidentally plug the numbers in the wrong places?<br><BR>\n" );
document.write( "Assuming you are a student just starting to learn algebra, it is best if you work the problem using basic ideas.<br><BR>\n" );
document.write( "To find the slope of the line, I strongly recommend using \"rise over run\" with a mental (or paper and pencil) sketch of the given points -- instead of using the ubiquitous formula for calculating the slope.<br><BR>\n" );
document.write( "The run (change in x) is 6, from -2 to 4; the rise is 8, from -3 to 5.  So the slope \"rise over run\" is 8/6 or 4/3.<br><BR>\n" );
document.write( "Then I think the most instructional way to find the equation is to use the slope-intercept form of the equation with one of the given points to find the intercept.  Using (x,y)=(4,5):<br><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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=%284%2F3%29%284%29%2Bb ALIGN=MIDDLE  ALT=\"5=%284%2F3%29%284%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=16%2F3%2Bb ALIGN=MIDDLE  ALT=\"5=16%2F3%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1%2F3 ALIGN=MIDDLE  ALT=\"b=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "One form of the equation is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x-1%2F3 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can of course write the equation in equivalent forms.  Multiplying by 3 to clear the fractions...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=4x-1 ALIGN=MIDDLE  ALT=\"3y=4x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y-1=0 ALIGN=MIDDLE  ALT=\"4x-3y-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y=1 ALIGN=MIDDLE  ALT=\"4x-3y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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