document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146815>Question 146815</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321067142/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find k so that the line through (4,-1) and (k,2) is<BR>\n" );
document.write( "a. parallel to 2x + 3y = 6<BR>\n" );
document.write( "b. perpendicular to 5x - 2y = -1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107217 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find k so that the line through (4,-1) and (k,2) is<BR>\n" );
document.write( "a. parallel to 2x + 3y = 6<BR>\n" );
document.write( "b. perpendicular to 5x - 2y = -1<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "a. Put in form y = mx+b to find the slope m<BR>\n" );
document.write( "y = (-2/3)x + 2<BR>\n" );
document.write( "m = -2/3<BR>\n" );
document.write( "To be parallel, the line has to have the same slope.<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "-2/3 = (2 - (-1))/(k - 4)<BR>\n" );
document.write( "-2/3 = 3/(k-4)<BR>\n" );
document.write( "-2(k-4) = 9<BR>\n" );
document.write( "-2k+8 = 9<BR>\n" );
document.write( "2k=-1<BR>\n" );
document.write( "k = -1/2<BR>\n" );
document.write( "Check: (2 + 1)/((-1/2) - 4) = 3/(-4.5) = -2/3<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "b. The slope m of 5x - 2y = -1 is 5/2.<BR>\n" );
document.write( "To be perpendicular, the slope is the negative inverse, -2/5.<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "-2/5 = (2+1)/(k-4)<BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "-2(k-4) = 5*3<BR>\n" );
document.write( "-2k+8 = 15<BR>\n" );
document.write( "2k = -7<BR>\n" );
document.write( "k = -7/2<BR>\n" );
document.write( "Check (2 + 1)/(-3.5 -4) = 3/(-7.5) = -2/5\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );