document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=576707>Question 576707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you graph a line with the slope of -3 passing through the point (2,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369986 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=369986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graphs look are easier to draw, and look best on graph paper or grid paper. Having all those little squares helps a lot.<BR>\n" );
document.write( "THE JUST DRAW APPROACH<BR>\n" );
document.write( "Your first step may be to draw a set of x-y axes and plot the point (2,2).<BR>\n" );
document.write( "(If you are lucky, the graph may turn out nice without too much work).<BR>\n" );
document.write( "At the beginning it would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-2%2C8%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C2%2C0.2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Then you could use the slope to plot other points.<BR>\n" );
document.write( "The slope is usually a rational number, like 3/5, or -2/7, or 1, or -3. That slope number is the ratio of \"rise\" (units moving up) to \"run\" (units moving to the right). A slope of  2/3 would mean that moving up 2 units and to the right 3 units you can locate another point.<BR>\n" );
document.write( "For your line, a slope of -3=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F1 ALIGN=MIDDLE  ALT=\"%28-3%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that you move up by -3 units (meaning move down by 3 units) as you move right by 1 unit to locate the next point, like this (but do not draw the arrows):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-2%2C8%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C2%2C0.2%29%29%2C%0D%0Ared%28arrow%282.2%2C2%2C2.2%2C-0.8%29%29%2C+red%28arrow%282.2%2C-0.8%2C3%2C-0.8%29%29%2C%0D%0Ared%28circle%283%2C-1%2C0.15%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > You can connect those two points with a straight line and hope for the best.<BR>\n" );
document.write( "For a better graph, you may want to keep going like that, plotting more points, and/or reverse course and go in the opposite direction, plotting more points.<BR>\n" );
document.write( "AT some point you may realize that it would be more convenient to have a different scale for your x and y axes. (I just did).<BR>\n" );
document.write( "You may end up with something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-8%2C12%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C2%2C0.2%29%29%2C%0D%0Ared%28circle%283%2C-1%2C0.2%29%29%2C%0D%0Ared%28circle%284%2C-4%2C0.2%29%29%2C%0D%0Ared%28circle%285%2C-7%2C0.2%29%29%2C%0D%0Ablue%28circle%281%2C5%2C0.2%29%29%2C%0D%0Ablue%28circle%280%2C8%2C0.2%29%29%2C%0D%0Ablue%28circle%28-1%2C11%2C0.2%29%29%2C%0D%0Aline%28-2%2C14%2C6%2C-10%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "THE CAREFUL PLANNING APPROACH<BR>\n" );
document.write( "You may want to make a table with x and y values, so you can carefully plan the scale on your x and y axes. It could be done as above, but you would calculate a bunch of points before plotting.<BR>\n" );
document.write( "Starting with (x,y)=(2,2), you would add -3 to the y as you add 1 to the x to get points (3,-1), (4,-4), (5,-7), (6,-10).<BR>\n" );
document.write( "Then you would go the opposite way adding 3 to the y as you add -1 to the x to get points (1,5), (0,8), (-1,11), (-2,14).<BR>\n" );
document.write( "With all those points you would decide to draw the x axis from -2 to 6 and the y axis from -10 to 14, and then you may mark points (6,-10), and (-2,14), connect them with a straight line, verify that (2,2) is on that line, and congratulate yourself for a beautiful graph.<BR>\n" );
document.write( "You could instead write the equation for the line (maybe in point-slope form), and pick your scales and end-points from there. </SPAN>\n" );
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