document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956088>Question 956088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Which set of points lies on the given graph?\r<BR>\n" );
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document.write( "(Points : 1)<BR>\n" );
document.write( "       (4, 11), (–2, 7), (1, –1)<BR>\n" );
document.write( "       (4, 11), (2, –7), (1, 1)<BR>\n" );
document.write( "       (–4, 11), (–2, 7), (1, –1)<BR>\n" );
document.write( "       (–4, 11), (–2, 7), (1, 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584142 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=584142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> check which ones lie in a line:\r<BR>\n" );
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document.write( "(4, 11), (–2, 7), (1, –1)\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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( "  <BR>\n" );
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" );
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document.write( "  <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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X1,Y1) and (X2,Y2) is<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%287-11%29%2F%28-2-4%29%29+=+0.666666666666667 ALIGN=MIDDLE  ALT=\"slope+=+%28%287-11%29%2F%28-2-4%29%29+=+0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X3,Y3) and (X1,Y1) is<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%28-1-11%29%2F%281-4%29%29+=+4 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-1-11%29%2F%281-4%29%29+=+4\"   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 3 points do not a same line. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Here the slopes are unequal hence the points do not lie on same line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
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document.write( "NOT an answer\r<BR>\n" );
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document.write( "(4, 11), (2, –7), (1, 1)\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
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document.write( "  <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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X1,Y1) and (X2,Y2) is<BR>\n" );
document.write( "  <BR>\n" );
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( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%28-7-11%29%2F%282-4%29%29+=+9 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-7-11%29%2F%282-4%29%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X3,Y3) and (X1,Y1) is<BR>\n" );
document.write( "  <BR>\n" );
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%281-11%29%2F%281-4%29%29+=+3.33333333333333 ALIGN=MIDDLE  ALT=\"slope+=+%28%281-11%29%2F%281-4%29%29+=+3.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(2)<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  From conditions (1) and (2)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The 3 points do not a same line. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Here the slopes are unequal hence the points do not lie on same line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
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document.write( "(–4, 11), (–2, 7), (1, –1)\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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( "  <BR>\n" );
document.write( "  <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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X1,Y1) and (X2,Y2) is<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%287-11%29%2F%28-2--4%29%29+=+-2 ALIGN=MIDDLE  ALT=\"slope+=+%28%287-11%29%2F%28-2--4%29%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X3,Y3) and (X1,Y1) is<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%28-1-11%29%2F%281--4%29%29+=+-2.4 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-1-11%29%2F%281--4%29%29+=+-2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(2)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  From conditions (1) and (2)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The 3 points do not a same line. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Here the slopes are unequal hence the points do not lie on same line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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( "  <BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \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" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X1,Y1) and (X2,Y2) is<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%287-11%29%2F%28-2--4%29%29+=+-2 ALIGN=MIDDLE  ALT=\"slope+=+%28%287-11%29%2F%28-2--4%29%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Slope of line taking points (X3,Y3) and (X1,Y1) is<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%281-11%29%2F%281--4%29%29+=+-2 ALIGN=MIDDLE  ALT=\"slope+=+%28%281-11%29%2F%281--4%29%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(2)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  From conditions (1) and (2)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The slopes are equal hence the 3 points can lie on same line.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%281-7%29%2F%281--2%29%29+=+-2 ALIGN=MIDDLE  ALT=\"slope+=+%28%281-7%29%2F%281--2%29%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(3)<BR>\n" );
document.write( "  <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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
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document.write( "your answer is:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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