document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922400>Question 922400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value(s) of k will the lines <BR>\n" );
document.write( "kx+5y=2 and 2x+(k+3)y=4 be:\r<BR>\n" );
document.write( "\n" );
document.write( "a) parallel to each other?    b)perpendicular to each other </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559561 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For what value(s) of k will the lines<BR>\n" );
document.write( "kx+5y=2 and 2x+(k+3)y=4 be: a) parallel to each other?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "put both equations in the slope intercept form<BR>\n" );
document.write( "kx + 5y = 2<BR>\n" );
document.write( "5y = -kx + 2<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k%2F5 ALIGN=MIDDLE  ALT=\"-k%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "2x + (k+3)y = 4<BR>\n" );
document.write( "(k+3)y = -2x + 4<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%28%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"-2%2F%28%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"4%2F%28%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the slope of parallel lines are equal; therefore\<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k%2F5 ALIGN=MIDDLE  ALT=\"-k%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%28%28K%2B3%29%29 ALIGN=MIDDLE  ALT=\"-2%2F%28%28K%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "-k(k+3) = 5 * -2<BR>\n" );
document.write( "-k(k+3) = -10<BR>\n" );
document.write( "multiply both sides by -1<BR>\n" );
document.write( "k(k+3) = 10<BR>\n" );
document.write( "k^2 + 3k - 10 = 0<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(k+5)(k-2) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "k = 2<BR>\n" );
document.write( "the negative solution will also work<BR>\n" );
document.write( "k = -5<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b)perpendicular to each other<BR>\n" );
document.write( "the relationship of slopes of perpendicular lines: m1 * m2 = -1, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k%2F5 ALIGN=MIDDLE  ALT=\"-k%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%28%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"-2%2F%28%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%29%2F%285%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282k%29%2F%285%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%29%2F%28%285k%2B15%29%29 ALIGN=MIDDLE  ALT=\"%282k%29%2F%28%285k%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1<BR>\n" );
document.write( "2k = -1(5k+15)<BR>\n" );
document.write( "2k = -5k - 15<BR>\n" );
document.write( "2k + 5k = -15<BR>\n" );
document.write( "7k = -15<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15%2F7 ALIGN=MIDDLE  ALT=\"-15%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > value for perpendicular lines<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );