document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250932>Question 250932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y = 3   what is the slope for this line?<BR>\n" );
document.write( "X = -2  what is the slope for this line?<BR>\n" );
document.write( "Are they perpendicular? Explain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182697 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=182697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the slope for y = 3 is 0.\r<BR>\n" );
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document.write( "the slope for x = -2 is undefined.\r<BR>\n" );
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document.write( "they are perpendicular to each other because the slope of 1 is a negative reciprocal of the other.\r<BR>\n" );
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document.write( "negative reciprocal of a slope is equal to -1 divided by the slope.\r<BR>\n" );
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document.write( "negative reciprocal of 0 is equal to -1/0 which is undefined.\r<BR>\n" );
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document.write( "since the slopes of the 2 lines follow the rules for being negative reciprocals of each other, then the lines are perpendicular to each other.\r<BR>\n" );
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document.write( "standard form of the equation of a line is ax + by = c\r<BR>\n" );
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document.write( "y = 3 converted to this form is equivalent to:\r<BR>\n" );
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document.write( "0*x + 1*y = 3\r<BR>\n" );
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document.write( "x = -2 converted to this form is equivalent to:\r<BR>\n" );
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document.write( "1*x + 0*y = -2\r<BR>\n" );
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document.write( "since the terms being multiplied by 0 cancel out, these equations become:\r<BR>\n" );
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document.write( "y = 3 and x = -2\r<BR>\n" );
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document.write( "the equations you are seeing are in standard form.\r<BR>\n" );
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document.write( "the slope intercept form of these equations is:\r<BR>\n" );
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document.write( "y = m*x + b where:\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( "we will convert the standard form of these equations to slope intercept form so show you what is happening with the slope.\r<BR>\n" );
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document.write( "we will take the original standard form before the canceling out of the terms.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "0*x + 1*y = 3\r<BR>\n" );
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document.write( "1*x + 0*y = -2\r<BR>\n" );
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document.write( "to convert these, you solve for y in both equations.\r<BR>\n" );
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document.write( "the first equation is:\r<BR>\n" );
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document.write( "0*x + 1*y = 3\r<BR>\n" );
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document.write( "subtract 0*x from both sides of the equation to get:\r<BR>\n" );
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document.write( "1*y = -0*x + 3\r<BR>\n" );
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document.write( "divide both sides of this equation by 1 to get:\r<BR>\n" );
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document.write( "y = (-0/1)*x + (3/1)\r<BR>\n" );
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document.write( "this is in slope intercept form with m*x = (-0/1)*x, so the slope is equal to (-0/1) which is equivalent to 0.\r<BR>\n" );
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document.write( "y = 3 is equivalent to standard form of 0*x + 1*y = 3 which is equivalent to slope intercept form of y = 0*x + 3 with a slope of 0.\r<BR>\n" );
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document.write( "the second equation is:\r<BR>\n" );
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document.write( "1*x + 0*y = -2\r<BR>\n" );
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document.write( "subtract 1*x from both sides of this equation to get:\r<BR>\n" );
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document.write( "0*y = -1*x - 2\r<BR>\n" );
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document.write( "divide both sides of this equation by 0 to get:\r<BR>\n" );
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document.write( "y = (-1/0)*x - (2/0)\r<BR>\n" );
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document.write( "this is in slope intercept form with m*x = (-1/0)*x, so the slope is equal to (-1/0) which is undefined.\r<BR>\n" );
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document.write( "x = -2 is equivalent to standard form of 1*x + 0*y = -2 which is equivalent to slope intercept form of y = (-1/0)*x - (2/0) with a slope that is undefined.\r<BR>\n" );
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document.write( "note that the y-intercept is equal to (2/0) which is also undefined.   \r<BR>\n" );
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document.write( "a slope of (-1/0) is the negative reciprocal of a slope of 0 meaning that y = 3 and x = -2 are perpendicular to each other.\r<BR>\n" );
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document.write( "y = 3 is a horizontal line 3 units above the x-axis.\r<BR>\n" );
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document.write( "x = -2 is a vertical line 2 units to the left of the y-axis.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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