document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167928>Question 1167928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of the line through (2, 3) that is perpendicular to the line with<BR>\n" );
document.write( "equation x = -1 also goes through which point? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792518 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=792518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the line with equation x = -1 is a vertical line.\r<BR>\n" );
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document.write( "when x = -1, the value of y can be any real value.\r<BR>\n" );
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document.write( "(-1,0) is on the line.<BR>\n" );
document.write( "(-1,3) is on the line.<BR>\n" );
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document.write( "the slope of a vertical line is undefined.\r<BR>\n" );
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document.write( "that's because the slope of a straight line is the change in the value of y divided by the corresponding change in the value of x.\r<BR>\n" );
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document.write( "since x is always equal to -1, there is no change in the value of x, meaning the change in the value of x is equal to 0.\r<BR>\n" );
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document.write( "this means that the denominator in the equation of change in the value of y divided by the change in the value of x is equal to the change in the value of y divided by 0, the result of which is undefined.\r<BR>\n" );
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document.write( "the line perpendicular to the vertical line has a slope that is a negative reciprocal of the slope of the vertical line.\r<BR>\n" );
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document.write( "if the slope of the vertical line is the change in the value of y divided by 0, then the slope of the line perpendicular to it is equal to 0 divided by the negative value of the change in the value of y.\r<BR>\n" );
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document.write( "the slope of the horizontal line is therefore equal to 0, because 0 divided by anything is equal to 0.\r<BR>\n" );
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document.write( "that means the line is horizontal.\r<BR>\n" );
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document.write( "the slope intercept form of the equation of a straight line is y = mx + b\r<BR>\n" );
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document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "with a slope of 0, the equation of the horizontal line is therefore y = 0 * x + b\r<BR>\n" );
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document.write( "solve for b by replacing x and y with their respective values from any point on the line.\r<BR>\n" );
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document.write( "when the line goes through the point (x,y) = (2,3), replace x with 2 and y with 3 to get:\r<BR>\n" );
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document.write( "y = 0 * x + b becomes:\r<BR>\n" );
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document.write( "3 = 0 * 2 + b\r<BR>\n" );
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document.write( "simplify to get b = 3\r<BR>\n" );
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document.write( "the equation of the line perpendicular to the vertical line is therefore:\r<BR>\n" );
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document.write( "y = 0 * x + 3 which simplifies to y = 3.\r<BR>\n" );
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document.write( "the graph of both lines is shown below:\r<BR>\n" );
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document.write( "you can see from the graph that the lines intersect at the point (x,y) = (-1,3) and that the point (x,y) = (2,3) is on the horizontal line.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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