document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=541232>Question 541232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plot the points A(1,3) and B(2,5)<BR>\n" );
document.write( "work out the gradient of AB\r<BR>\n" );
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document.write( "this the question in my home work, i do not understand<BR>\n" );
document.write( "Please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354136 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Gradient (or grade) is a word sometimes used for what we call the \"slope\" of a line.<BR>\n" );
document.write( "We define slope as the ratio of the increase in the y-coordinate (sometimes called rise or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA ALIGN=MIDDLE  ALT=\"DELTA\"   DISABLED_style= \"max-width:90%; height:auto;\" >y)<BR>\n" );
document.write( "and the increase in the x-coordinate (sometimes called run or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA ALIGN=MIDDLE  ALT=\"DELTA\"   DISABLED_style= \"max-width:90%; height:auto;\" >x).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-1%2C+6%2C+-1%2C+6%2C%0D%0A++grid%28+1+%29%2C%0D%0A++red%28+circle%28+1%2C+3%2C+0.1+%29+%29%2C%0D%0A++red%28+circle%28+2%2C+5%2C+0.1+%29+%29%2C%0D%0A++red%28line%28+1%2C+3%2C+2%2C5+%29%29%2C%0D%0A++blue%28line%28+1%2C+3%2C+2%2C3+%29%29%2C%0D%0A++green%28line%28+2%2C+3%2C+2%2C5+%29%29%2C%0D%0A++locate%28+1.2%2C+3%2C+run+%29%2C%0D%0A++locate%28+2.1%2C+4%2C+rise+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > I plotted the points and drew the segment AB in red. I colored the run blue and the rise green.<BR>\n" );
document.write( "So to calculate the gradient, you count the units to the right (run), and the units up (rise) going from one point to the other, then divide <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gradient=+rise%2Frun ALIGN=MIDDLE  ALT=\"gradient=+rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For this problem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gradient=+2%2F1=2 ALIGN=MIDDLE  ALT=\"gradient=+2%2F1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sometimes, it is calculated without plotting, so instead of visualizing the rise and run, it is calculated by difference from the coordinates of the points:<BR>\n" );
document.write( "For this problem, we could have calculated, without plotting:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gradient=+rise%2Frun=%285-3%29%2F%282-1%29=2%2F1=2 ALIGN=MIDDLE  ALT=\"gradient=+rise%2Frun=%285-3%29%2F%282-1%29=2%2F1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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