document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=576060>Question 576060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Are the following two lines parallel? 3x + 4y = 4 2x - 6y = 7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369715 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=369715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to be parallel, the graphs of each of these two equations must have the same slope.<BR>\n" );
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document.write( "To find the slopes, let's convert each equation to the slope intercept form. That form is:<BR>\n" );
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document.write( "y = mx + b<BR>\n" );
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document.write( "and m, which is the multiplier of x, is the slope of the graph. (b is the value at which the graph crosses the y-axis.)<BR>\n" );
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document.write( "So let's look at the first equation and let's solve it for y.<BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "3x + 4y = 4<BR>\n" );
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document.write( "Get rid of the 3x on the left side by subtracting 3x from both sides. With that subtraction the equation becomes:<BR>\n" );
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document.write( "4y = -3x + 4<BR>\n" );
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document.write( "Now solve for y by dividing both sides of this equation (all terms) by 4. This results in:<BR>\n" );
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document.write( "y = (-3/4)x + 4/4<BR>\n" );
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document.write( "and the 4/4 results in 1, so the equation becomes:<BR>\n" );
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document.write( "y = (-3/4)x + 1<BR>\n" );
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document.write( "By comparing this to the slope intercept form you can see that m, the slope, is the multiplier of x and it is -3/4.<BR>\n" );
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document.write( "Now, lets do the same thing for the second equation. <BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "2x - 6y = 7<BR>\n" );
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document.write( "Get rid of the 2x on the left side by subtracting 2x from both sides to get:<BR>\n" );
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document.write( "-6y = -2x + 7<BR>\n" );
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document.write( "Solve for y by dividing both sides (all terms) by -6 and the equation becomes:<BR>\n" );
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document.write( "y = (-2/-6)x + 7/(-6)<BR>\n" );
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document.write( "This time the multiplier of the x is (-2/-6) which reduces to +1/3. ( b is equal to -7/6)<BR>\n" );
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document.write( "So for one equation we have the slope equal to -3/2 and for the other equation the slope is +1/3. The two slopes are not the same. Therefore, the graphs have to cross somewhere. And since they cross at some point they are not parallel.<BR>\n" );
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document.write( "You now have the answer and there is nothing else that you need to do.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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