document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206576>Question 206576</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1405802111/algebrahomeworkh>Longman mathematics for IGCSE Book1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\">  The line joining (-2,1) to (6,4), is parallel to the line joining (-q,5) to (4,q). Find the value of q.\r<BR>\n" );
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document.write( "It would certainly be a great pleasure for me if you solve my question. <BR>\n" );
document.write( "Thank you very much indeed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156126 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156126\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the lines are parallel then their slopes have to be equal.<BR>\n" );
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document.write( "your slope is given by the equation (y2-y1)/(x2-x1)<BR>\n" );
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document.write( "your first line joins (-2,1) to (6,4)<BR>\n" );
document.write( "y2 - y1 = 4 - 1 = 3<BR>\n" );
document.write( "x2 - x1 = 6 - (-2) = 8<BR>\n" );
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document.write( "the slope of your first line is 3/8<BR>\n" );
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document.write( "your second line joins (-q,5) to (4,q)<BR>\n" );
document.write( "for the slopes to be equal, y2-y1 / x2-x1 must equal 3/8<BR>\n" );
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document.write( "y2-y1 = q-5<BR>\n" );
document.write( "x2-x1 = 4-(-q) = q + 4<BR>\n" );
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document.write( "(q-5)/(q+4) must equal 3/8<BR>\n" );
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document.write( "if we multiply both sides of this equation by 8 we get:<BR>\n" );
document.write( "(8q-40)/(q+4) = 3<BR>\n" );
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document.write( "if we multiply both sides of this equation by (q+4) we get:<BR>\n" );
document.write( "8q-40 = 3q + 12<BR>\n" );
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document.write( "if we subtract 3q from both sides of this equation and we add 40 to both sides of this equation we get:<BR>\n" );
document.write( "5q = 52<BR>\n" );
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document.write( "if we divide both sides of this equation by 5 we get:<BR>\n" );
document.write( "q = (52/5)<BR>\n" );
document.write( "this is equivalent to 10.4<BR>\n" );
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document.write( "our first line passes through the points (-2,1) and (6,4)<BR>\n" );
document.write( "our second line passes through the points (-10.4,5) and (4,10.4)<BR>\n" );
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document.write( "if both lines have the same slope, then the slope of the second line should equal (3/8)<BR>\n" );
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document.write( "the slope of the second line is y2-y1/x2-x1 = (10.4 - 5)/(4 - (-10.4))<BR>\n" );
document.write( "this comes out to be 5.4/14.4<BR>\n" );
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document.write( "5.4/14.4 is the same ratio as 3/8 so the slopes are the same.<BR>\n" );
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document.write( "our answer is q = 10.4<BR>\n" );
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document.write( "to graph these equations, we need to get them into the standard form of y = mx + b<BR>\n" );
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document.write( "m is the slope = 3/8<BR>\n" );
document.write( "b is the y intercept which is the value of y when x = 0<BR>\n" );
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document.write( "to find b, we substitute one of the points in the equation and solve for b.<BR>\n" );
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document.write( "for the first equation, we will use the point (6,4)<BR>\n" );
document.write( "y = mx + b becomes 4 = 6*(3/8) + b<BR>\n" );
document.write( "this makes b = 1.75<BR>\n" );
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document.write( "standard form of our first equation is y = (3/8)*x + 1.75<BR>\n" );
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document.write( "for the second equation, we will use the point (4,10.4)<BR>\n" );
document.write( "y = mx + b becomes 10.4 = 4*(3/8) + b<BR>\n" );
document.write( "this makes b = 8.9<BR>\n" );
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document.write( "standard form of our second equation is y = (3/8)*x + 8.9<BR>\n" );
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document.write( "graph of both equations looks like the following:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-12%2C8%2C-2%2C12%2C%283%2F8%29%2Ax+%2B+1.75%2C%283%2F8%29%2Ax+%2B+8.9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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