document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947844>Question 947844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which kind of function best models the set of data points:<BR>\n" );
document.write( "-1,22  0,6   1,-10     2,-26  and 3,-42?\r<BR>\n" );
document.write( "\n" );
document.write( "linear<BR>\n" );
document.write( "quadratic<BR>\n" );
document.write( "exponential<BR>\n" );
document.write( "non e of the above\r<BR>\n" );
document.write( "\n" );
document.write( "my answer is linear </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578449 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=578449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first check if they lie in a line:\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%286-22%29%2F%280--1%29%29+=+-16 ALIGN=MIDDLE  ALT=\"slope+=+%28%286-22%29%2F%280--1%29%29+=+-16\"   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%28-10-22%29%2F%281--1%29%29+=+-16 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-10-22%29%2F%281--1%29%29+=+-16\"   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%28-10-6%29%2F%281-0%29%29+=+-16 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-10-6%29%2F%281-0%29%29+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(3)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  From (1),(2) and (3)<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%28-26--42%29%2F%282-3%29%29+=+-16 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-26--42%29%2F%282-3%29%29+=+-16\"   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%28-10--42%29%2F%281-3%29%29+=+-16 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-10--42%29%2F%281-3%29%29+=+-16\"   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%28-10--26%29%2F%281-2%29%29+=+-16 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-10--26%29%2F%281-2%29%29+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(3)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  From (1),(2) and (3)<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since all points lie in a line, choose two of them and find  linear equation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=change_this_name10094.solver>Find the equation of line going through points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, -10) and (x2, y2) = (0, 6).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%286--10%29%2F%280-1%29+=+-16 ALIGN=MIDDLE  ALT=\"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%286--10%29%2F%280-1%29+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2A1+%2Bb+=+6 ALIGN=MIDDLE  ALT=\"-16%2A1+%2Bb+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-10--16%2A1+=+6 ALIGN=MIDDLE  ALT=\"b=-10--16%2A1+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  y=(-16)x + (6)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Your graph:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C%0D%0A++++graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+-16%2Ax%2B6+%29%2C%0D%0A++++red%28+locate%28+1%2C+-10%2C+%221%2C+-10%22+%29%2C+circle%28+1%2C+-10%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+0%2C+6%2C+%220%2C+6%22+%29%2C+circle%28+0%2C+6%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, answer is: linear </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );