document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083363>Question 1083363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please explain how this is done, I want to be able to do this without help\r<BR>\n" );
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document.write( "Write an equation in&#8203; slope-intercept form of the line satisfying the following conditions through &#8203;(6&#8203;,9&#8203;); perpendicular to x=5\r<BR>\n" );
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document.write( "The equation of the line ______<BR>\n" );
document.write( "&#8203;(Type an equation. Type your answer in&#8203; slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your&#8203; answer.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697350 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=697350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> point is (6,9)<BR>\n" );
document.write( "line is perpendicular to vertical line x = 5.<BR>\n" );
document.write( "that means the line has to be horizontal.<BR>\n" );
document.write( "that means the slope of the line is 0<BR>\n" );
document.write( "that means the equation of the line is y = 9\r<BR>\n" );
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document.write( "the slope intercept form of the line would be y = 0*x + 9<BR>\n" );
document.write( "0*x goes away and you are left with y = 9\r<BR>\n" );
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document.write( "here's a graph of both equations.<BR>\n" );
document.write( "the intersection of the vertical line and the horizontal line is (5,9).\r<BR>\n" );
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document.write( "if the line y = 9 is perpendicular to the line x = 5, their sloped have to be negative reciprocals of each other.\r<BR>\n" );
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document.write( "the slope of the line y = 9 is equal to 0.\r<BR>\n" );
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document.write( "the slope of the line x = 5 is undefined.\r<BR>\n" );
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document.write( "a slope of 0 can have anything as the denominator because 0 divided by anything is equal to 0.\r<BR>\n" );
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document.write( "assuming the slope is 0/5, then the negative reciprocal would be -5/0 which is undefined.\r<BR>\n" );
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document.write( "how do you get an undefined slope?\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( "to convert to the slope intercept form, do the following:\r<BR>\n" );
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document.write( "start with ax + by = c\r<BR>\n" );
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document.write( "subtract ax from both sides of the equation to get by = c - ax\r<BR>\n" );
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document.write( "divide both sides of the equation by b to get y = c/b - ax/b\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get y = -ax/b + c/b\r<BR>\n" );
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document.write( "if b = 0, then the slope is undefined because you can't divide anything by 0 and get a real answer.\r<BR>\n" );
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document.write( "therefore, the standard form of the equation has to be ax + 0y = c\r<BR>\n" );
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document.write( "simplify this to get ax = c\r<BR>\n" );
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document.write( "divide both sides by a to get x = c/a\r<BR>\n" );
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document.write( "c/a is a constant, therefore x = c\r<BR>\n" );
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document.write( "how does this work with x = 5?\r<BR>\n" );
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document.write( "start with ax + by = c\r<BR>\n" );
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document.write( "set b = 0 to get ax = c\r<BR>\n" );
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document.write( "solve for x to get x = c/a\r<BR>\n" );
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document.write( "since you know that x = 5, then c/a must be equal to 5.\r<BR>\n" );
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document.write( "this could happen in muiltiple ways.\r<BR>\n" );
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document.write( "one way is that c = 25 and a = 5.\r<BR>\n" );
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document.write( "you would then start 5x + by = 25<BR>\n" );
document.write( "b is equal to 0 so you get 5x = 25<BR>\n" );
document.write( "divide both sides by 5 and you get x = 5.\r<BR>\n" );
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document.write( "the general rule is:\r<BR>\n" );
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document.write( "a vertical line is shown as x = c<BR>\n" );
document.write( "a horizontal line is y = c<BR>\n" );
document.write( "c is any constant.\r<BR>\n" );
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document.write( "how do we get a horizontal line?\r<BR>\n" );
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document.write( "start with ax + by = c\r<BR>\n" );
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document.write( "convert to slope intercept form to get y = -ax/b + c/b\r<BR>\n" );
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document.write( "-ax/b is equal to 0 when a is equal to 0.\r<BR>\n" );
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document.write( "go back to standard form and replace a with 0 to get 0x + by = c<BR>\n" );
document.write( "0x cancels out and you are left with by = c<BR>\n" );
document.write( "solve for y to get y = c/b\r<BR>\n" );
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document.write( "it can be a little complicated to get through, but, if you remember that a horizontal line is perpendicular to a vertical line, then the solution is pretty clear.\r<BR>\n" );
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