document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201136>Question 201136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph each equation or inequality\r<BR>\n" );
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document.write( "1.  y = 3/5 - 4\r<BR>\n" );
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document.write( "2. 4x - y =2\r<BR>\n" );
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document.write( "3.  x = -4\r<BR>\n" );
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document.write( "4. y = 2x - 5\r<BR>\n" );
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document.write( "5.  f(x) = 3x - 1\r<BR>\n" );
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document.write( "6. f(x) = [[3x]] = 3\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151883 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=151883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello....\r<BR>\n" );
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document.write( "Your first equation you wrote as:  y = 3/5 - 4.\r<BR>\n" );
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document.write( "I'm pretty sure you meant to say:  y = 3/5x - 4.\r<BR>\n" );
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document.write( "Under that assumption, I will tell you this:\r<BR>\n" );
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document.write( "Your equation is in the slope/intercept form for an equation of a line.  That means that the equation follows this format:   y = mx + b.   When you have a line in that format, then you know that \"m\" represents the slope of the line and \"b\" represents the y intercept.\r<BR>\n" );
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document.write( "Let's take this a step at a time then.....\r<BR>\n" );
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document.write( "If you want to find your \"y\" intercept, you solve for \"y\" by making \"x\" equal to 0.\r<BR>\n" );
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document.write( "So..... y = 3/5x - 4<BR>\n" );
document.write( "        y = 3/5(0) - 4<BR>\n" );
document.write( "        y = 0      - 4<BR>\n" );
document.write( "        y = -4\r<BR>\n" );
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document.write( "In other words, if \"x\" equals 0, then \"y\" equals -4.   Therefore, you just found the first point on your graph and that point is (0, -4).  Now what?\r<BR>\n" );
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document.write( "Well, you have to look at your slope.   Your slope, remember, is represented by \"m\" in your equation.  So let's look at that:\r<BR>\n" );
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document.write( "y =   mx + b<BR>\n" );
document.write( "y = 3/5x - 4\r<BR>\n" );
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document.write( "What is \"m\" in the above?  Do you see that \"m\" is 3/5?  Therefore, your slope is 3/5.  \r<BR>\n" );
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document.write( "Do you know that slope is defined as RISE over RUN.  (I'm not sure how to write that in this space, but think of RISE over RUN as a fraction --- rise/run).\r<BR>\n" );
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document.write( "So your 3 is the RISE and the 5 is the RUN.  Three tells you to go UP three spaces from your point located at (0, -4) and then after you go up 3, you should go over 5 spaces.   \r<BR>\n" );
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document.write( "(If 3 had been NEGATIVE, you would have gone DOWN three spaces - watch out for positives and negatives).\r<BR>\n" );
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document.write( "Sooooo, now your graph has the point (0, -4)and the 2nd point that is 3 up and 5 over from (0, -4)   That new point is located at (5, -1).  If you just \"connect the dots\" you will have your graph of a line.\r<BR>\n" );
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document.write( "Your 2nd problem is:\r<BR>\n" );
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document.write( "4x - y = 2 \r<BR>\n" );
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document.write( "All you need to do is put this equation in the y = mx + b format.  In other words, solve for y.  Let's try it:\r<BR>\n" );
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document.write( "4x - y = 2\r<BR>\n" );
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document.write( "4x - 4x - y = 2 - 4x  (subtract 4x from both sides)<BR>\n" );
document.write( "        - y = 2 - 4x  (see how we got rid of the 4x on the left side?)<BR>\n" );
document.write( "          y = -2 + 4x (divide both sides by -1)\r<BR>\n" );
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document.write( "          y = 4x - 2  (rearrange the problem so that it is in the <BR>\n" );
document.write( "                       correct format)\r<BR>\n" );
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document.write( "Now, you can graph this as you did the above problem.  Do you see your \"y\" intercept?  Make x = 0 and solve for y.  That means your first point is:  \r<BR>\n" );
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document.write( "(0, -2)\r<BR>\n" );
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document.write( "What is your slope?  Well, \"m\" equals 4, which is the same as 4/1, so remembering that the slope is rise over run, we can see that we must \"rise\" 4 spaces up, and \"run\" 1 space over from the point (0, -2).  Then you just connect those two points on the graph and you'll have your line.\r<BR>\n" );
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document.write( "For your 3rd problem, you had to solve x = - 4.   Here's something to know:\r<BR>\n" );
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document.write( "When x equals a number, the line is VERTICAL on the graph.  The slope is UNDEFINED.\r<BR>\n" );
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document.write( "When y equals a number, the line is HORIZONTAL on the graph.  The slope is 0.\r<BR>\n" );
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document.write( "Sooooo, x = -4 means that you draw a straight and vertical line that thru -4 on your coordinate plane.\r<BR>\n" );
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document.write( "Your 4th problem is in the y = mx + b format, so you should be able to do that by now.  :-)  \r<BR>\n" );
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document.write( "I hope this helps you.  Good luck!<BR>\n" );
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