document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=664366>Question 664366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . For the table that follows, answer the following questions:<BR>\n" );
document.write( "x	y<BR>\n" );
document.write( "1	1<BR>\n" );
document.write( "2	4<BR>\n" );
document.write( "3	7<BR>\n" );
document.write( "4	\r<BR>\n" );
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document.write( "-  Would the correlation between x and y in the table above be positive or negative?<BR>\n" );
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document.write( "-  Find the missing value of y in the table.<BR>\n" );
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document.write( "-  How would the values of this table be interpreted in terms of linear regression?<BR>\n" );
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document.write( "-  If a “line of best fit” is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?<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 #413298 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=413298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we will take two points and find equation of a line passing through\r<BR>\n" );
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document.write( "let points be (<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;\" >), and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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;\" >)\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=find_equation_of_line.solver>FIND EQUATION of straight line given 2 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, 1) and (x2, y2) = (3, 7).<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+=+%287-1%29%2F%283-1%29+=+3 ALIGN=MIDDLE  ALT=\"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%287-1%29%2F%283-1%29+=+3\"   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=3%2A1+%2Bb+=+-2 ALIGN=MIDDLE  ALT=\"3%2A1+%2Bb+=+-2\"   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=1-3%2A1+=+-2 ALIGN=MIDDLE  ALT=\"b=1-3%2A1+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  y=(3)x + (-2)<BR>\n" );
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document.write( "  Your graph:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3%2Ax%2B-2+%29%2C%0D%0A++++red%28+locate%28+1%2C+1%2C+%221%2C+1%22+%29%2C+circle%28+1%2C+1%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+3%2C+7%2C+%223%2C+7%22+%29%2C+circle%28+3%2C+7%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so, equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x+-2 ALIGN=MIDDLE  ALT=\"y=3x+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....and the slope of this line is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "now check if all points lie on same line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Ccircle%281%2C1%2C0.2%29%2Ccircle%282%2C4%2C0.2%29%2Ccircle%283%2C7%2C0.2%29%2Ccircle%280%2C0%2C0.0%29%2Cgraph%28600%2C600%2C-10%2C10%2C-10%2C10%2C3x+-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see,  all points do lie on same line\r<BR>\n" );
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document.write( "now we can calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <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;\" > using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x+-2 ALIGN=MIDDLE  ALT=\"y=3x+-2\"   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=3%2A4+-2 ALIGN=MIDDLE  ALT=\"y=3%2A4+-2\"   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=12+-2 ALIGN=MIDDLE  ALT=\"y=12+-2\"   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=10 ALIGN=MIDDLE  ALT=\"y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........the missing value\r<BR>\n" );
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document.write( "so, your table is:\r<BR>\n" );
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document.write( "x|	y<BR>\n" );
document.write( "1|	1<BR>\n" );
document.write( "2|	4<BR>\n" );
document.write( "3|	7<BR>\n" );
document.write( "4|	10\r<BR>\n" );
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document.write( "now check if a point (<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=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >) also lie on a line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C15%2Cgrid%281%29%2Ccircle%281%2C1%2C0.2%29%2Ccircle%282%2C4%2C0.2%29%2Ccircle%283%2C7%2C0.2%29%2Ccircle%284%2C10%2C0.2%29%2Cgraph%28600%2C600%2C-10%2C10%2C-10%2C15%2C3x+-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-correlation would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >% because every point fit on the line\r<BR>\n" );
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