document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261712>Question 261712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is this a linear equation how would you solve this problem y-4x=5 step by step </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192841 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=192841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y-4x=5 \r<BR>\n" );
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document.write( "The above is your equation.  \r<BR>\n" );
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document.write( "What if you put that equation in a SLOPE INTERCEPT form of an equation?   The slope intercept form of an equation is:  y = mx + b.\r<BR>\n" );
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document.write( "What do those letters mean?  Well, m refers to the SLOPE of a graph.  The b refers to the y-intercept.  Those are more vocabulary words but don't get intimidated.  Let's take this a step at a time.\r<BR>\n" );
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document.write( "First, let's put this equation in the y = mx + b format.  All this means is that we are going to solve for y.  Here goes:\r<BR>\n" );
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document.write( "y - 4x = 5  Let's add \"4x\" to both sides of the equation to isolate \"y\".<BR>\n" );
document.write( "y = 4x + 5  <------This is in the y = mx + b format, which is:   <BR>\n" );
document.write( "y = mx + b\r<BR>\n" );
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document.write( "The \"m\" as you can see, is 4.  <BR>\n" );
document.write( "The \"b\" as you can see, is 5.  What do we do with this info?  Well....\r<BR>\n" );
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document.write( "The \"m\" is the slope - the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rise%2Frun ALIGN=MIDDLE  ALT=\"rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the equation.<BR>\n" );
document.write( "The \"b\" - the y intercept - and you can think of that as a point on a graph where you first pin down your line.  Let me explain.....\r<BR>\n" );
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document.write( "A coordinate plane looks like a cross right?  The horizontal line is 'x' and the vertical line is 'y'.   The \"y intercept\" that I'm talking about above is where a point \"bumps into\" (intercepts) the vertical \"y\" line.  In this case, the \"b\" equals 5.  That means on the y line (the y axis) you count five spaces UP (up is positive) on the coordinate plane.  \r<BR>\n" );
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document.write( "Now draw a dot on the y line at that point that was five spaces up.  That is where you can pin down the first part of your line.  That point, which is five spaces up, is technically at (0, 5).  \r<BR>\n" );
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document.write( "Ok... now what?  Now you look at your slope, which was the \"m\" in your equation.  In this case, m = 4.  Every number can be written as a fraction, yes?  So the number 4, if written as a fraction would be:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F1 ALIGN=MIDDLE  ALT=\"4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Writing the slope as:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F1 ALIGN=MIDDLE  ALT=\"4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > lets us think about the slope as is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284for+the+RISE%29%2F%281+for+the+RUN%29 ALIGN=MIDDLE  ALT=\"%284for+the+RISE%29%2F%281+for+the+RUN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By rise, I mean, from the starting point (which in this case is (0, 5), you will RISE up 4 spaces and you will RUN (horizontally) to the right 1 space.  The new point that is created is located at (1, 9).   \r<BR>\n" );
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document.write( "If you take a ruler and draw a line that connects (0, 5) and (1, 9), you will see your line that is created.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+900%2C+900%2C+-20%2C+20%2C+-20%2C+20%2C+4x+%2B+5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+900%2C+900%2C+-20%2C+20%2C+-20%2C+20%2C+4x+%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now just to give you some extra info:  IF IF IF (!) the slope had been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F1 ALIGN=MIDDLE  ALT=\"%28-4%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you would have counted DOWN 4 spaces from the (0, 5) starting point.  You see, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RISE%2FRUN ALIGN=MIDDLE  ALT=\"RISE%2FRUN\"   DISABLED_style= \"max-width:90%; height:auto;\" > might make you think that with the word \"rise\" you will always go up a certain number of spaces.  That would not be true.  RISE means that you can go up OR down on the y line (the y axis) of the coordinate plane.  The direction you take depends on whether you have a positive or negative number.  Positive numbers go UP.  Negative numbers go DOWN.\r<BR>\n" );
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document.write( "Similarly, for the RUN portion of the slope, you can RUN left, or you can RUN right.  Positive numbers run to the right on the x line (the x axis) and negative numbers run to the left on the x axis.\r<BR>\n" );
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document.write( "I hope this helps you. :-) </SPAN>\n" );
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