document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403757>Question 403757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the graph, determine the value of y when x=4.\r<BR>\n" );
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document.write( "The graph shows a forward slanting line the crosses -3 on the y-axis and 1.5 on x axis..\r<BR>\n" );
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document.write( "how do i figure this out? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285472 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=285472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "given:\r<BR>\n" );
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document.write( "Using the graph, determine the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <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( "line the crosses <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis ALIGN=MIDDLE  ALT=\"y-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >...means you have one point at (0,-3)\r<BR>\n" );
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document.write( " and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > axis....means you have second point at (1.5, 0)\r<BR>\n" );
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document.write( "now, we can find EQUATION of straight line given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > points\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) = (0, -3) and (x2, y2) = (1.5, 0).<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+=+%280--3%29%2F%281.5-0%29+=+2 ALIGN=MIDDLE  ALT=\"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%280--3%29%2F%281.5-0%29+=+2\"   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=2%2A0+%2Bb+=+-3 ALIGN=MIDDLE  ALT=\"2%2A0+%2Bb+=+-3\"   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=-3-2%2A0+=+-3 ALIGN=MIDDLE  ALT=\"b=-3-2%2A0+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  y=(2)x + (-3)<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+2%2Ax%2B-3+%29%2C%0D%0A++++red%28+locate%28+0%2C+-3%2C+%220%2C+-3%22+%29%2C+circle%28+0%2C+-3%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+1.5%2C+0%2C+%221.5%2C+0%22+%29%2C+circle%28+1.5%2C+0%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( "from the graph you can see, if you draw a line parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis ALIGN=MIDDLE  ALT=\"y-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the 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;\" > it will cross your line at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <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;\" >; your third point is (4,5)\r<BR>\n" );
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document.write( "let's check if all three your points are collinear (lie on 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( "  <BR>\n" );
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%280--3%29%2F%281.5-0%29%29+=+2 ALIGN=MIDDLE  ALT=\"slope+=+%28%280--3%29%2F%281.5-0%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  <BR>\n" );
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%285--3%29%2F%284-0%29%29+=+2 ALIGN=MIDDLE  ALT=\"slope+=+%28%285--3%29%2F%284-0%29%29+=+2\"   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( "  <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" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%285-0%29%2F%284-1.5%29%29+=+2 ALIGN=MIDDLE  ALT=\"slope+=+%28%285-0%29%2F%284-1.5%29%29+=+2\"   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( "  <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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