document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945144>Question 945144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Are the graphs of the lines in the pair parallel? Explain.\r<BR>\n" );
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document.write( "y = 3x + 10\r<BR>\n" );
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document.write( "12x – 3y = –36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576325 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lines with equal slopes are parallel, so put the equations in slope intercept form (y=mx+b, m is the slope)<BR>\n" );
document.write( "y=3x+10 This equation is in correct form, and has a slope=3<BR>\n" );
document.write( "12x – 3y = –36 Add 3y to each side<BR>\n" );
document.write( "12x=3y-36 Add 36 to each side<BR>\n" );
document.write( "12x+36=3y Divide each side by 3<BR>\n" );
document.write( "4x+12=y Reverse sides of equation for clarity<BR>\n" );
document.write( "y=4x+12  This equation has slope=4, which is not parallel to a line with slope=3<BR>\n" );
document.write( "ANSWER No, the lines are not parallel.<BR>\n" );
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document.write( "---OR--- <BR>\n" );
document.write( "If the lines have a common solution, they intersect and therefore are not parallel<BR>\n" );
document.write( "Solve each equation for y and set the two equal (we've solved for y above)<BR>\n" );
document.write( "y=3x+10<BR>\n" );
document.write( "y=4x+12<BR>\n" );
document.write( "3x+10=4x+12 Subtract 3x from each side<BR>\n" );
document.write( "10=x+12 Subtract 12 from each side<BR>\n" );
document.write( "-2=x<BR>\n" );
document.write( "y=3(-2)+10<BR>\n" );
document.write( "y=4<BR>\n" );
document.write( "(-2,4) is a solution to this equation<BR>\n" );
document.write( "12x-3y=-36<BR>\n" );
document.write( "12(-2)-3(4)=-36<BR>\n" );
document.write( "-24-12=-36<BR>\n" );
document.write( "-36=-36<BR>\n" );
document.write( "(-2.4) is also a solution to this equations, so the lines intersect,thus they are NOT parallel </SPAN>\n" );
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