document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156674>Question 156674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to know how to solve & graph this linear equation: x-y=-3\r<BR>\n" );
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document.write( "Pleas help!!\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115494 by </B><A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><B>mangopeeler07(462)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><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=115494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x-y=-3\r<BR>\n" );
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document.write( "First, you want to isolate y to get this thing in y=mx+b form.\r<BR>\n" );
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document.write( "x-y=-3\r<BR>\n" );
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document.write( "Subtract x from each side<BR>\n" );
document.write( "-y=-x-3\r<BR>\n" );
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document.write( "Divide both sides by -1<BR>\n" );
document.write( "y=x+3\r<BR>\n" );
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document.write( "Now you have your equation for the line in y=mx+b form.  m=slope, and b=y-intercept.  Therefore, your slope here is 1 (since x is the same as 1x), and your y-intercept is 3.\r<BR>\n" );
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document.write( "Now to graph it, there are many different ways.  I'll show you two ways to do it:\r<BR>\n" );
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document.write( "1) Take the equation y=x+3 and plug in a value for x. Any value.  Say 3.<BR>\n" );
document.write( "y=3+3<BR>\n" );
document.write( "y=6\r<BR>\n" );
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document.write( "So one point to plot is (3,6).\r<BR>\n" );
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document.write( "Now plug in another random number, like 2.<BR>\n" );
document.write( "y=2+3<BR>\n" );
document.write( "y=5\r<BR>\n" );
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document.write( "(2,5)\r<BR>\n" );
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document.write( "Now how about -1?<BR>\n" );
document.write( "y=-1+3<BR>\n" );
document.write( "y=2\r<BR>\n" );
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document.write( "(-1,2)\r<BR>\n" );
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document.write( "And one point you already know is (0,3) because of the y intercept.\r<BR>\n" );
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document.write( "Now plot the points and draw a line through all four of them:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+x+%2B+-1+y+=+-3 ALIGN=MIDDLE  ALT=\"1+x+%2B+-1+y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-1%2F-1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-1%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. -3/1 = -3.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/-1 = 3.</LI><LI>Slope is -1/-1 = 1.</LI><LI> Equation in slope-intercept form: y=1*x+3.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+3-8%2C+3%2B8%2C+1%2Ax%2B3+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+3-8%2C+3%2B8%2C+1%2Ax%2B3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "Now the next way I'm going to show you, in my opinion, is an over-complicated brain fart.  But I will show it to you anyway, just in case it will be easier for you to do it this way (maybe).\r<BR>\n" );
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document.write( "2)Look at the equation y=x+3.<BR>\n" );
document.write( "Your slope=the change in y/change in x.  In other words, in this case, 1/1.  Your y-intercept is 3.\r<BR>\n" );
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document.write( "Start at the point (0,3).<BR>\n" );
document.write( "Since the change in y is 1, move up one.<BR>\n" );
document.write( "Since the change in x is 1, move to the right one.\r<BR>\n" );
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document.write( "(Does this feel like a board game yet?)\r<BR>\n" );
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document.write( "Now plot the point.  \r<BR>\n" );
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document.write( "Repeat the process.\r<BR>\n" );
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document.write( "Now go back to (0,3).  Since your slope can also be considered -1/-1, your change in y can be -1.  So move down one.\r<BR>\n" );
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document.write( "Same applies to your change in x.  It can be -1.  So move to the left 1.\r<BR>\n" );
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document.write( "Plot the point.\r<BR>\n" );
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document.write( "Repeat the process.\r<BR>\n" );
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document.write( "Draw a line through the points. (Now we're doing a Connect-the-dots)\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+x+%2B+-1+y+=+-3 ALIGN=MIDDLE  ALT=\"1+x+%2B+-1+y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-1%2F-1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-1%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. -3/1 = -3.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/-1 = 3.</LI><LI>Slope is -1/-1 = 1.</LI><LI> Equation in slope-intercept form: y=1*x+3.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+3-8%2C+3%2B8%2C+1%2Ax%2B3+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+3-8%2C+3%2B8%2C+1%2Ax%2B3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "I hope this helped you!<BR>\n" );
document.write( "-Alani </SPAN>\n" );
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