document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249951>Question 249951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me solve this\r<BR>\n" );
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document.write( "Exploration<BR>\n" );
document.write( "a) Write a linear equation in two variables that is<BR>\n" );
document.write( "satisfied by (3, 5).<BR>\n" );
document.write( "b) Write another linear equation in two variables that is<BR>\n" );
document.write( "satisfied by (3, 5).<BR>\n" );
document.write( "c) Are your equations independent or dependent?<BR>\n" );
document.write( "d) Explain how to select the second equation so that it will<BR>\n" );
document.write( "be independent of the first. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182029 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=182029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) When x=3, y=5.<BR>\n" );
document.write( "y = 5/3x works.<BR>\n" );
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document.write( "b) We could pick the perpendicular line by setting the slope to the negative inverse of 5/3<BR>\n" );
document.write( "y = -3/5x + b<BR>\n" );
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document.write( "We will have to solve 'b' to be sure the line goes through the point (3,5). <BR>\n" );
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document.write( "Substituting x=3 and y=5 (our known point), we have:<BR>\n" );
document.write( "5 = -3/5(3) + b<BR>\n" );
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document.write( "Multiplying through we have...<BR>\n" );
document.write( "5 = -9/5 + b<BR>\n" );
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document.write( "Adding 9/5 to both sides...<BR>\n" );
document.write( "5 + 9/5 = b<BR>\n" );
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document.write( "Simplifying...<BR>\n" );
document.write( "b = 5 + 1.8 = 6.8<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "y = -3/5(x) + 6.8<BR>\n" );
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document.write( "c) Perpendicular lines are independent.<BR>\n" );
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document.write( "d) Any line that has a slope different from 5/3 that goes through the point (3,5) will be independent and consistent.  it does not have to be perpendicular, just not parallel.  A parallel line going through the point will be identical to the line itself, so it will be dependent.<BR>\n" );
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document.write( "Graphing the two equations is a good check:<BR>\n" );
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