document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100873>Question 100873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the slope of the line 2x-5y=3<BR>\n" );
document.write( "Can you help me get this?\r<BR>\n" );
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document.write( "a)2<BR>\n" );
document.write( "b)-5<BR>\n" );
document.write( "c)5/2<BR>\n" );
document.write( "d)2/5<BR>\n" );
document.write( "e)-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73446 by </B><A HREF=/tutors/aboutme.mpl?userid=TP><B>TP(29)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TP><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=73446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To do this question you must be aware of the following.\r<BR>\n" );
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document.write( "The general equation of a straight line is written as y=mx+c where m is the slope(or gradient)of the line and c is the y coordinate where the line cuts the y axis( c is also called the y intercept).\r<BR>\n" );
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document.write( "In the more difficult questions you must also know how to re-arrange equations.<BR>\n" );
document.write( "Here is a simple example.<BR>\n" );
document.write( "Suppose the equation of a straight line is y=3x+2.<BR>\n" );
document.write( "If we compare this to the general equation y=mx+c then we can see that the number next to x(called the coefficient of x) is 3 in our equation and this is in the place taken up by m in the general equation.<BR>\n" );
document.write( "So we can say that m=3. But m is the slope of the line so the slope of the line that has equation y=3x+2 is 3.<BR>\n" );
document.write( "Also comparing both equations we can see that c=2. This means that the line with equation y=3x+2 cuts(or crosses) the vertical  y axis at 2 units up from the origin.\r<BR>\n" );
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document.write( "Examples: The line with equation y=5x+7 has a slope of 5 and and cuts the y axis at 7 up.<BR>\n" );
document.write( "The line with equation y=-4x-3 has a gradient of -4 and cuts the y axis at -3(3 below the origin).\r<BR>\n" );
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document.write( "So to identify the slope and the y coordinate where a line crosses the y axis your equation must be in the form y=mx+c.<BR>\n" );
document.write( "If the equation you are given is not in this form then you have to re-arrange it so that it is in the form y=mx+c.<BR>\n" );
document.write( "Example: Find the slope of the straight line that has the equation 4y-9x=12<BR>\n" );
document.write( "So 4y-9x=12 has to be re-arranged into the form y=mx+c before we can say what its slope is.<BR>\n" );
document.write( "Solution: Given 4y-9x=12<BR>\n" );
document.write( "Add 9x to both sides<BR>\n" );
document.write( "This gives 4y=12+9x or 4y=9x+12.<BR>\n" );
document.write( "But we need to have just y(or 1y) by itself on the left-hand side of the equal sign.<BR>\n" );
document.write( "To get this we must now share(divide)both sides of the equation 4y=9x+12 by 4.<BR>\n" );
document.write( "When we do this we get that 4y/4=9x/4+12/4.<BR>\n" );
document.write( "This simplifies to: y=2.25x+3 (since 9/4=2.25)<BR>\n" );
document.write( "So now we have the equation in the form y=mx+c and we can see that the number next to the x is 2.25 so the slope of the line is 2.25ANS.\r<BR>\n" );
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document.write( "Now for your equation 2x-5y=3. <BR>\n" );
document.write( "If we add 5y to both sides of the equation we get: 2x-5y+5y=3+5y<BR>\n" );
document.write( "This simplifies to 2x=3+5y or 2x=5y+3<BR>\n" );
document.write( "Now swap sides to get: 5y+3=2x<BR>\n" );
document.write( "We now need to get rid of the +3 on the left-hand side so that we are just left with 5y on the left-hand side.<BR>\n" );
document.write( "To do this we must subtract 3 from both sides so that we get:5y+3-3=2x-3.<BR>\n" );
document.write( "This simplifies to 5y=2x-3.<BR>\n" );
document.write( "(We're neally there, just one more step!)<BR>\n" );
document.write( "We need to have just y or 1y(same thing) on the left-hand side and so that 5 next to the y has to be changed to a 1.<BR>\n" );
document.write( "We do this by sharing(dividing)both sides by 5 so that we get: 5y/5=2x/5-3/5.<BR>\n" );
document.write( "This simplifies to y=0.4x-0.6 (since 5/5=1, 2/5=0.4 and 3/5=0.6).\r<BR>\n" );
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document.write( "So we (finally) have y=0.4x-0.6.<BR>\n" );
document.write( "This means that the slope of your line is 0.4 and it cuts the y axis at 0.6 below the origin (below because its -0.6 in the equation and not +0.6).\r<BR>\n" );
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document.write( "So looking at the list of answers that you have to choose from for the slope the correct answer is d)2/5 (since 0.4=2/5). </SPAN>\n" );
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