document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014504>Question 1014504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line 2x-y=5 turns about the point on it, whose ordinate and abscissae are equal, through an angle of 45°, in anti clockwise direction. Find the equation of line in the new position </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630781 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=630781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not sure how you're supposed to solve this, but this is how i did it.\r<BR>\n" );
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document.write( "your original equation is 2x - y = 5\r<BR>\n" );
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document.write( "solve for y to get y = 2x - 5\r<BR>\n" );
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document.write( "since the slope intercept form of the equation of a straight line is y = mx + b, and the slope is m and the y-intercept is b, then your slope is 2.\r<BR>\n" );
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document.write( "that's also the tangent of the angle between your line and a horizontal line that goes through any point on your line.\r<BR>\n" );
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document.write( "so you have tangent (theta) = 2.\r<BR>\n" );
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document.write( "that makes the angle theta equal to 63.42494882 degrees.\r<BR>\n" );
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document.write( "now you are at the point (5,5).\r<BR>\n" );
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document.write( "draw a horizontal line through it and draw the line of your equation through it.\r<BR>\n" );
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document.write( "now, if you rotate that line an additional 45 degrees in an anti-clockwise direction, the angle between the horizontal line and your new line will be 65... + 45 = 108.4349494882 degrees.\r<BR>\n" );
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document.write( "that means that the tangent of your new line will be tangent (108.4349494882).\r<BR>\n" );
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document.write( "solve for that to get your new tangent equals -3.\r<BR>\n" );
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document.write( "that means the slope of your new line is equal to -3.\r<BR>\n" );
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document.write( "the slope intercept form of an equation for a straight line is y = mx + b\r<BR>\n" );
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document.write( "m is the slope and b is the y intercept.\r<BR>\n" );
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document.write( "when the slope is -3, the equation becomes y = -3x + b\r<BR>\n" );
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document.write( "you need to find b.\r<BR>\n" );
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document.write( "when y = -3x + b goes through the point (5,5), you can replace y with 5 and x with 5 to get:\r<BR>\n" );
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document.write( "5 = -3*5 + b\r<BR>\n" );
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document.write( "solve for b to get b = 20\r<BR>\n" );
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document.write( "the equation of your new line is y = -3x + 20.\r<BR>\n" );
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document.write( "it will intersect with your oirignal line at (5,5) and the angle between it and the original line will be 45 degrees.\r<BR>\n" );
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document.write( "the graph of your original line and the new line is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/011902.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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