document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253949>Question 253949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a linear equation.\r<BR>\n" );
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document.write( "y = 1/2x + 1\r<BR>\n" );
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document.write( "Part a\r<BR>\n" );
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document.write( "Complete this table of values for the equation.\r<BR>\n" );
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document.write( "                   Input X           Output Y\r<BR>\n" );
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document.write( "                    -4/\r<BR>\n" );
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document.write( "                    -2/\r<BR>\n" );
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document.write( "                     0\r<BR>\n" );
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document.write( "                     2\r<BR>\n" );
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document.write( "                     4\r<BR>\n" );
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document.write( "These are the values that I came up with for the Y output\r<BR>\n" );
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document.write( "                     -4/    -1\r<BR>\n" );
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document.write( "                     -2/     0\r<BR>\n" );
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document.write( "                      0/     1\r<BR>\n" );
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document.write( "                      2/     2\r<BR>\n" );
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document.write( "                      4/     3\r<BR>\n" );
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document.write( "I hope that I have the Y output values correct.  Do I?\r<BR>\n" );
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document.write( "The problem is that I now have to graph the equation which I did complete,<BR>\n" );
document.write( "but I want to make sure that I did it correctly.\r<BR>\n" );
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document.write( "I don't know if anyone can put a graph on here so that I can see if mine is<BR>\n" );
document.write( "correct.\r<BR>\n" );
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document.write( "This is how I plotted the points on my X and Y axis graph.\r<BR>\n" );
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document.write( "I looked at the points and plotted them like this  (-4/-01)<BR>\n" );
document.write( "                                                    (-2/0)<BR>\n" );
document.write( "                                                     (0,1)<BR>\n" );
document.write( "                                                      (2,2)<BR>\n" );
document.write( "                                                       (4,3)\r<BR>\n" );
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document.write( "It ended up looking like the slope of a mountain from the lower left being the<BR>\n" );
document.write( "lowest and gradually increasing as a slope.\r<BR>\n" );
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document.write( "Can you please tell me if my output values are correct, and the way I handled<BR>\n" );
document.write( "graphing the values.\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 #186317 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your values are right but you made it harder than it really is.<BR>\n" );
document.write( "You may have heard the expression that the a straight line is the shortest distance between two points.<BR>\n" );
document.write( "It is also true that to draw a straight line you only need two points.<BR>\n" );
document.write( "The two easiest point to find are when  x=0 and when y=0<BR>\n" );
document.write( "your equation <BR>\n" );
document.write( "y=1/2*x+1<BR>\n" );
document.write( "when x=0 y=1<BR>\n" );
document.write( "when y=0 x=?\r<BR>\n" );
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document.write( "You have it your list.<BR>\n" );
document.write( "notice something special about your line<BR>\n" );
document.write( "It has a slant of 1/2 which means everytime that y goes up by 1 x goes up by 2.<BR>\n" );
document.write( "It is not  a coincidence that your equation has a 1/2 in it. That is called the slope like a ski slope which means the slant or incline.<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=-0.5+x+%2B+1+y+=+1 ALIGN=MIDDLE  ALT=\"-0.5+x+%2B+1+y+=+1\"   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+=+--0.5%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--0.5%2F1\"   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. 1/-0.5 = -2.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 1/1 = 1.</LI><LI>Slope is --0.5/1 = 0.5.</LI><LI> Equation in slope-intercept form: y=0.5*x+1.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+1-8%2C+1%2B8%2C+0.5%2Ax%2B1+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+1-8%2C+1%2B8%2C+0.5%2Ax%2B1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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