document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458436>Question 458436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the linear equation y = 3/4x-2, find the y-coordinates of the points (-8,  ), (-4,  ), and (4,  ). Please show all of your work. Plot those points and graph the linear equation.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314511 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=314511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Given the linear equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29x-2 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-coordinates ALIGN=MIDDLE  ALT=\"y-coordinates\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the points \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29%28-8%29-2=-24%2F4-2=-6-2=-8 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29%28-8%29-2=-24%2F4-2=-6-2=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29%28-4%29-2=-12%2F4-2=-3-2=-5 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29%28-4%29-2=-12%2F4-2=-3-2=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29%284%29-2=12%2F4-2=3-2=1 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29%284%29-2=12%2F4-2=3-2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-coordinates ALIGN=MIDDLE  ALT=\"y-coordinates\"   DISABLED_style= \"max-width:90%; height:auto;\" > are\r<BR>\n" );
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document.write( "(-8, -8 ), (-4, -5 ), and (4,1  )\r<BR>\n" );
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document.write( "check if these <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > points lie in a same line\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=To_determine_if_3_points_lie_in_a_line.solver>To determine if 3 points lie in a line</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT> The 3 points lie on a same plane. For all points to lie on a line they should satisfy the <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/Polynomial-Expressions-and-Equations-in-Color.lesson>equation of a line</A>. Hence any two points taken on a line should calculate to the same slope of a line.<BR>\n" );
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document.write( "  In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Graphs/slope.wikipedia>slope</A>. <BR>\n" );
document.write( "  Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.<BR>\n" );
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document.write( "  Slope of line taking points (X1,Y1) and (X2,Y2) is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28Y2-Y1%29%2F%28X2-X1%29 ALIGN=MIDDLE  ALT=\"slope+=+%28Y2-Y1%29%2F%28X2-X1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%28-5--8%29%2F%28-4--8%29%29+=+0.75 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-5--8%29%2F%28-4--8%29%29+=+0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
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document.write( "  Slope of line taking points (X3,Y3) and (X1,Y1) is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28Y3-Y1%29%2F%28X3-X1%29 ALIGN=MIDDLE  ALT=\"slope+=+%28Y3-Y1%29%2F%28X3-X1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%281--8%29%2F%284--8%29%29+=+0.75 ALIGN=MIDDLE  ALT=\"slope+=+%28%281--8%29%2F%284--8%29%29+=+0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(2)<BR>\n" );
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document.write( "  From conditions (1) and (2)<BR>\n" );
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document.write( "  The slopes are equal hence the 3 points can lie on same line.<BR>\n" );
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document.write( "  If the slope calculated from points (X2,Y2) and (X3,Y3) comes out to be same then it is confirmed that the 3 points lie on a same line.<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28Y3-Y2%29%2F%28X3-X2%29 ALIGN=MIDDLE  ALT=\"slope+=+%28Y3-Y2%29%2F%28X3-X2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%281--5%29%2F%284--4%29%29+=+0.75 ALIGN=MIDDLE  ALT=\"slope+=+%28%281--5%29%2F%284--4%29%29+=+0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(3)<BR>\n" );
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document.write( "  From (1),(2) and (3)<BR>\n" );
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document.write( "  Hence, It is proved that the 3 points lie on same line.<BR>\n" );
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document.write( "  To read more on equations of a line refer to articles on <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Graphs/Graphing-by-Slope-Intercept-Method.lesson>wikipedia</A><BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "let's see the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F4%29x-2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F4%29x-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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