document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27578>Question 27578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> L has y-intercept(0,2) and is perpendicular to the line with equation 2x-3y=6. I have a hard time with problems like these. please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14990 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> questions like these are straight forward... just need to build it up slowly.\r<BR>\n" );
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document.write( "Line L has an equation of the form y=mx+c...we need to find m, the gradient , and c - the y-intercept. The question will give you the info somewhere. You just need to find it :-)\r<BR>\n" );
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document.write( "So, first, gradient.<BR>\n" );
document.write( "The Q says that L is perpendicular to the other line quoted. Perpendicular means that they are at right angles to each other. Now, the gradients of 2 lines that are perpendicular (call the gradients m and n) multiply to give -1, so we can use this fact to find the gradient of L.\r<BR>\n" );
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document.write( "First, what is the gradient of the other line?\r<BR>\n" );
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document.write( "2x-3y=6<BR>\n" );
document.write( "2x = 3y+6<BR>\n" );
document.write( "or 3y+6 = 2x<BR>\n" );
document.write( "3y = 2x-6<BR>\n" );
document.write( "y = (2/3)x-2\r<BR>\n" );
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document.write( "so its gradient is (2/3)\r<BR>\n" );
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document.write( "So our gradient, call it m, is -(3/2) which is found from: m*n = -1\r<BR>\n" );
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document.write( "--> m*(2/3) = -1<BR>\n" );
document.write( "--> m = -(3/2)\r<BR>\n" );
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document.write( "So, our equation is y = -(3/2)x + c<BR>\n" );
document.write( "Now we need to find the value of c. To do this, we need to know a set of values of (x,y) on the line. We are given this... (0,2)\r<BR>\n" );
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document.write( "so, y = -(3/2)x + c becomes<BR>\n" );
document.write( "2 = -(3/2)*0 + c<BR>\n" );
document.write( "2 = 0 + c<BR>\n" );
document.write( "--> c = 2\r<BR>\n" );
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document.write( "so, the equation of L is y = -(3/2)x + 2 which is an answer. We can get rid of the fraction, giving 2y = -3x + 4 and then possibly move the x too to give 2y + 3x = 4.\r<BR>\n" );
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document.write( "Any of these versions is correct.\r<BR>\n" );
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document.write( "Hope that helps\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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