document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072408>Question 1072408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the slope of a line parallel and perpendicular to this line?<BR>\n" );
document.write( "2×+3y=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687325 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=687325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have the standard form of the equation, which is ax + by = c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a is the coefficient of x<BR>\n" );
document.write( "b is the coefficient of y<BR>\n" );
document.write( "c is the constant\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to convert this to the slope intercept form of y = mx + b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the conversion works as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with 2x + 3y = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 2x from both sides of the equation to get 3y = 1 - 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "reorder the terms in descending order of degree to get 3y = -2x + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 3 to get y = -2/3 * x + 1/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the slope intercept form of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-2/3 is equal to the slope which is equal to m in the general equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1/3 is equal to the y-intercept which is equal to b in the general equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a line parallel to this line will have the same slope but a different y-intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of this line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we can pick any y-intercept not equal to 1/3 for the parallel line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we can pick any y-intercept, including 1/3, for the perpendicular line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equations i chose to display are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = -2/3 * x + 1/3 for the original line\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = -2/3 * x + 5 for the parallel line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 3/2 * x - 10 for the perpendicular line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of all 3 equations is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/031102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the line of the original equation is blue.<BR>\n" );
document.write( "the line of the parallel equation is red.<BR>\n" );
document.write( "the line of the perpendicular equation is orange.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );