document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826947>Question 826947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the line passing through the points <BR>\n" );
document.write( "(a, 1) and (&#8722;10, 9)<BR>\n" );
document.write( " is parallel to the line passing through the points <BR>\n" );
document.write( "(&#8722;3, 8) and (a + 2, 1),<BR>\n" );
document.write( " what is the value of a? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503884 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two parallel lines<BR>\n" );
document.write( "one through (a,1) and (-10,9) and another through (-3,8) and (a+2,1)<BR>\n" );
document.write( "Since parallel lines have the same slope we can<BR>\n" );
document.write( "use the general equation for slope<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For (a,1) and (-10,9) , x1=a x2=-10 y1=1 y2=9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-1%29%2F%28-10-a%29 ALIGN=MIDDLE  ALT=\"%289-1%29%2F%28-10-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-10-a%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-10-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For (-3,8) and (a+2,1) , x1=-3 x2=a+2 y1=8 y2=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-8%29%2F%28%28a%2B2%29-%28-3%29%29 ALIGN=MIDDLE  ALT=\"%281-8%29%2F%28%28a%2B2%29-%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28a%2B2%29%2B3%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28a%2B2%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28a%2B5%29%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28a%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now set the two slope equations to be equal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28a%2B5%29%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28a%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-10-a%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-10-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "do cross products<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28-10-a%29=8%28a%2B5%29 ALIGN=MIDDLE  ALT=\"7%28-10-a%29=8%28a%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-70 -7a = 8a + 40<BR>\n" );
document.write( "add 70 to each side<BR>\n" );
document.write( " -7a = 8a + 110<BR>\n" );
document.write( "add -8a to each side<BR>\n" );
document.write( " -15a = 110<BR>\n" );
document.write( "divide each side by -15<BR>\n" );
document.write( "a = -110/15<BR>\n" );
document.write( "a = -22/3<BR>\n" );
document.write( "Checking <BR>\n" );
document.write( "For (a,1) and (-10,9) , x1=a x2=-10 y1=1 y2=9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-1%29%2F%28-10-a%29 ALIGN=MIDDLE  ALT=\"%289-1%29%2F%28-10-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >?= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-10-a%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-10-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with a = -22/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-1%29%2F%28-10-%28-22%2F3%29%29 ALIGN=MIDDLE  ALT=\"%289-1%29%2F%28-10-%28-22%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >?= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-10-%28-22%2F3%29%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-10-%28-22%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "?= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-10%2B22%2F3%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-10%2B22%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-30%2F3%2B22%2F3%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-30%2F3%2B22%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2F%28-8%2F3%29 ALIGN=MIDDLE  ALT=\"%288%29%2F%28-8%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -3<BR>\n" );
document.write( "So we have the slope for the first set of points = -3<BR>\n" );
document.write( "Let's look at the second set.<BR>\n" );
document.write( "For (-3,8) and (a+2,1) , x1=-3 x2=a+2 y1=8 y2=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-8%29%2F%28%28a%2B2%29-%28-3%29%29 ALIGN=MIDDLE  ALT=\"%281-8%29%2F%28%28a%2B2%29-%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28a%2B2%29%2B3%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28a%2B2%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28a%2B5%29%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28a%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with a = -22/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-8%29%2F%28%28%28-22%2F3%29%2B2%29-%28-3%29%29 ALIGN=MIDDLE  ALT=\"%281-8%29%2F%28%28%28-22%2F3%29%2B2%29-%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28%28-22%2F3%29%2B6%2F3%29%2B3%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28%28-22%2F3%29%2B6%2F3%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2F%28%28%28-22%2F3%29%2B6%2F3%29%2B9%2F3%29 ALIGN=MIDDLE  ALT=\"%287%29%2F%28%28%28-22%2F3%29%2B6%2F3%29%2B9%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28-7%2F3%29 ALIGN=MIDDLE  ALT=\"7%2F%28-7%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= -3<BR>\n" );
document.write( "So we see that a = -22/3 produces two lines with the same -3 slope.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );