document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=579434>Question 579434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve and graph this? Please HELP!!\r<BR>\n" );
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document.write( "   y-3=3(x-2)   and    y=6x-12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371071 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=371071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Linear equations graph as straight lines. All you need is two good points for each line. Choosing your points is an art, and you get better with practice.<BR>\n" );
document.write( "The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=3%28x-2%29 ALIGN=MIDDLE  ALT=\"y-3=3%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is expressed in a form known as the point-slope form.<BR>\n" );
document.write( "The slope of a line passing through point (2,3) and point (x,y) would be calculates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=%28y-3%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"slope=%28y-3%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=slope%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"y-3=slope%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=3%28x-2%29 ALIGN=MIDDLE  ALT=\"y-3=3%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation of a line that passes through (2,3) and has a slope of 3.<BR>\n" );
document.write( "You can plot the point (2,3) to start.<BR>\n" );
document.write( "Since the slope is increase in y (rise) divided by increase in x (run), starting from (2,3) you could run 1 space to the right and rise 3 spaces up to mark a second point for the line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-1%2C9%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C3%2C0.2%29%29%2Cred%28circle%283%2C6%2C0.2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Then you connect the points with a straight line. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-1%2C9%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C3%2C0.2%29%29%2Cred%28circle%283%2C6%2C0.2%29%29%2C%0D%0Agreen%28line%280%2C-3%2C4%2C9%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6x-12 ALIGN=MIDDLE  ALT=\"y=6x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given in slope intercept form.<BR>\n" );
document.write( "The coefficient of x, 6, is the slope and the constant -12 is the y-intercept, the y coordinate of the point where the line crosses the y-axis that is the line where x=0.<BR>\n" );
document.write( "That gives you point (0,-12) to start. Using the slope to run 1 unit right and rise 6 up from (0,-12) you would get to (1,-6) and repeating the running and rising, you would get to points (2,0) and (3,6).<BR>\n" );
document.write( "You can use any pair of those points to draw the second line, but I'd pick (2,0) and (3,6) because they fit in the graph I started before. And then I would connect them with a straight line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-1%2C9%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C3%2C0.2%29%29%2Cred%28circle%283%2C6%2C0.2%29%29%2C%0D%0Agreen%28line%280%2C-3%2C4%2C9%29%29%2C%0D%0Ablue%28circle%282%2C0%2C0.3%29%29%2C+blue%28circle%283%2C6%2C0.3%29%29%2C%0D%0Ablue%28line%281%2C-6%2C4%2C12%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > AT this point you may realize that the lines intersect at (3,60.<BR>\n" );
document.write( "The point (3,6) represents the solution to the system of linear equations: x=3 paired with y=6.<BR>\n" );
document.write( "It is good to verify by substituting those values in the equations, especially if the intersection is not one of your carefully calculated points. </SPAN>\n" );
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