document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233668>Question 233668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation in general form for the line that goes through (4, -1) and (4,5)\r<BR>\n" );
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document.write( "x=? \r<BR>\n" );
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document.write( "Thank you for your help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172479 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=172479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The points are (x,y) = (4,-1) and (4,5)\r<BR>\n" );
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document.write( "slope-intercept form of the line is y = mx + b where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "It appears you will have a vertical line.\r<BR>\n" );
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document.write( "Let's see what happens:\r<BR>\n" );
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document.write( "Slope is equal to (y2-y1) / (x2-x1)\r<BR>\n" );
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document.write( "(x1,y1) = (4,-1)<BR>\n" );
document.write( "(x2,y2) = (4,5)\r<BR>\n" );
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document.write( "y2-y1 = 5 - (-1) = 6<BR>\n" );
document.write( "x2-x1 = 5 - 4 = 0\r<BR>\n" );
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document.write( "(y2-y1) / (x2-x1) becomes 6/0 which is undefined.\r<BR>\n" );
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document.write( "This means that y can vary but x can't, so the line is vertical.\r<BR>\n" );
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document.write( "The equation of your line is x = 4\r<BR>\n" );
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document.write( "x will always be 4 and y can be any value.\r<BR>\n" );
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document.write( "How did this equation come about?\r<BR>\n" );
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document.write( "The standard form of the equation of a straight line is ax + by = c\r<BR>\n" );
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document.write( "a is the coefficient of the x term.<BR>\n" );
document.write( "b is the coefficient of the y term.<BR>\n" );
document.write( "c is the constant.\r<BR>\n" );
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document.write( "To convert the standard form to the slope-intercept form, you do the following:\r<BR>\n" );
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document.write( "Equation is:<BR>\n" );
document.write( "ax + by = c<BR>\n" );
document.write( "Subtract ax from both sides to get:<BR>\n" );
document.write( "by = -ax + c<BR>\n" );
document.write( "divide both sides by b to get:<BR>\n" );
document.write( "y = -ax/b + c/b\r<BR>\n" );
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document.write( "That's the same as the slope-intercept form of the equation of y = mx + b where m = the slope = (-a/b).\r<BR>\n" );
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document.write( "If b = 0, the slope is undefined.\r<BR>\n" );
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document.write( "If b = 0, the standard form of the equation of:\r<BR>\n" );
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document.write( "ax + by = c becomes:\r<BR>\n" );
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document.write( "ax + 0y = c which becomes:\r<BR>\n" );
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document.write( "ax = c\r<BR>\n" );
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document.write( "In your equation, a = 1 and c = 4 to get:\r<BR>\n" );
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document.write( "x = 4\r<BR>\n" );
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document.write( " </SPAN>\n" );
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