document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920021>Question 920021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am currently learning about the Rectangle Coordinate system and I am now looking for the equations using the Two-point form and the Point-slope form. We are required to present only one standard equation for all of our final answers.\r<BR>\n" );
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document.write( "The given points are (6,-4) and (8,-2) and the slope that I solved was 2/2 or 1. What should I do to make y= 6x-40 (equation after solving for point-slope) into 2x-2y-10=0(equation after solving for two-point) or vice versa? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558122 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your points are (6,-4) and (8,-2)\r<BR>\n" );
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document.write( "the formula for slope is (y2-y1) / (x2-x) which becomes:\r<BR>\n" );
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document.write( "slope = (-2--4) / (8-6) which becomes (-2+4) / 2 which becomes 2/2 which becomes 1.\r<BR>\n" );
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document.write( "the slope intercept form of the equation is y = mx + b<BR>\n" );
document.write( "you have m which is the slope, so your equation becomes y = x + b<BR>\n" );
document.write( "you now have to solve for b which is the y-intercept.\r<BR>\n" );
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document.write( "your points are (6,-4) and (8,-2).\r<BR>\n" );
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document.write( "you can use either point to solve for b.\r<BR>\n" );
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document.write( "2 ways to solve for b.\r<BR>\n" );
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document.write( "one way is to replace x and y with the values of one of the coordinates and solve for b.\r<BR>\n" );
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document.write( "for example, y = x + b becomes -4 = 6 + b when you replace y with -4 and x with 6.<BR>\n" );
document.write( "solve for b to get b = -4 - 6 = -10\r<BR>\n" );
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document.write( "y = mx + b becomes y = x - 10 which is the slope intercept form of the equation.\r<BR>\n" );
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document.write( "another way is to use the point slope form of the equation and use one of the points.\r<BR>\n" );
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document.write( "the point slope form of the equation is y - y1 = m(x - x1)\r<BR>\n" );
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document.write( "m = 1<BR>\n" );
document.write( "y1 = -4<BR>\n" );
document.write( "x1 = 6\r<BR>\n" );
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document.write( "point slope form of the equation is y + 4 = 1(x-6) which becomes:<BR>\n" );
document.write( "y + 4 = x-6<BR>\n" );
document.write( "subtract 4 from both sides of this equation to get:<BR>\n" );
document.write( "y = x - 10\r<BR>\n" );
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document.write( "that's the slope intercept form of the equation where m = 1 and b = -10.\r<BR>\n" );
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document.write( "now you have the slope intercept form of the equation and you want to convert that to the standard form of the equation.\r<BR>\n" );
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document.write( "standard form of the equation is ax + by = c\r<BR>\n" );
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document.write( "start with y = x - 10\r<BR>\n" );
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document.write( "subtract x from both sides of this equation to get:\r<BR>\n" );
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document.write( "y - x = -10\r<BR>\n" );
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document.write( "put the x in front of the y and you get:\r<BR>\n" );
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document.write( "-x + y = -10\r<BR>\n" );
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document.write( "it's not quite in standard form because the coefficient of the x term should be positive.\r<BR>\n" );
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document.write( "multiply both sides of the equation by -1 to get:\r<BR>\n" );
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document.write( "x - y = 10\r<BR>\n" );
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document.write( "now it's in standard form.\r<BR>\n" );
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document.write( "the other thing you need to consider is that the coefficients of x and y should be integers, so if you have fractional coefficients, you need to multiply both sides of the equation by a multiple so that the denominators disappear.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "if your equation was 1/3x + 2/4y = 6, then multiply both sides of the equation by a common multiple such as 12 and you will get 4x + 3y = 72\r<BR>\n" );
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document.write( "that doesn't apply to your problem since your coefficients are already integers.\r<BR>\n" );
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document.write( "your final equation is x - y = 10\r<BR>\n" );
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document.write( "to confirm this equation is correct, donvert it back into slope intercept form.\r<BR>\n" );
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document.write( "subtract x from both sides of the equation to get -y = -x + 10<BR>\n" );
document.write( "multiply both sides of the equation by -1 to get y = x - 10.\r<BR>\n" );
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document.write( "that was the original slope intercept frorm of the equation that you started with so you're good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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