document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133510>Question 133510</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3) Study the method of linear interpolation presented in chapter 5. Given p(x) = 2x^3 – 3x^2 – 6x + 4, show that there is an irrational root in the interval (0,1) and use linear interpolation to find the root accurate to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97679 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's find the possible rational roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3-3x%5E2-6x+%2B+4 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3-3x%5E2-6x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Any rational zero can be found through this equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE Roots=\frac{p}{q}\"> where p and q are the factors of the last and first coefficients\r<BR>\n" );
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document.write( "So let's list the factors of 4 (the last coefficient):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p=\pm1, \pm2, \pm4\">\r<BR>\n" );
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document.write( "Now let's list the factors of 2 (the first coefficient):\r<BR>\n" );
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document.write( "Now let's divide each factor of the last coefficient by each factor of the first coefficient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{1}, \frac{1}{2}, \frac{2}{1}, \frac{2}{2}, \frac{4}{1}, \frac{4}{2}, \frac{-1}{1}, \frac{-1}{2}, \frac{-2}{1}, \frac{-2}{2}, \frac{-4}{1}, \frac{-4}{2}\">\r<BR>\n" );
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document.write( "Now simplify\r<BR>\n" );
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document.write( "These are all the distinct rational zeros of the function that could occur\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  1, \frac{1}{2}, 2, 4, -1, \frac{-1}{2}, -2, -4\">\r<BR>\n" );
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document.write( "So the only possible rational roots in the interval (0,1) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. However, if we plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29 ALIGN=MIDDLE  ALT=\"f%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get \r<BR>\n" );
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document.write( "So we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <b>not</b> a zero of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3-3x%5E2-6x+%2B+4 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3-3x%5E2-6x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So there are no rational roots in the interval (0,1)\r<BR>\n" );
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document.write( "Now let's see if there is a zero in the interval (0,1)\r<BR>\n" );
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document.write( "Let's evaluate f(0) (the left endpoint of the interval)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3-3x%5E2-6x%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3-3x%5E2-6x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=2%280%29%5E3-3%280%29%5E2-6%280%29%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=2%280%29%5E3-3%280%29%5E2-6%280%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   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=f%280%29=2%2A0-3%2A0%5E2-6%2A0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=2%2A0-3%2A0%5E2-6%2A0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 0 to the 3rd power to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0-3%2A0%5E2-6%2A0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=0-3%2A0%5E2-6%2A0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 0 to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0-3%2A0-6%2A0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=0-3%2A0-6%2A0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 0 to the 2nd power to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0-0-6%2A0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=0-0-6%2A0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 and 0 to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0-6%2A0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=0-6%2A0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 0 from 0 to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0-0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=0-0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6 and 0 to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0%2B4 ALIGN=MIDDLE  ALT=\"f%280%29=0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 0 from 0 to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=4 ALIGN=MIDDLE  ALT=\"f%280%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 0 and 4 to get 4\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how y is positive)\r<BR>\n" );
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document.write( "Now let's evaluate f(1) (the right endpoint of the interval)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3-3x%5E2-6x%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3-3x%5E2-6x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2%281%29%5E3-3%281%29%5E2-6%281%29%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=2%281%29%5E3-3%281%29%5E2-6%281%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   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=f%281%29=2%2A1-3%2A1%5E2-6%2A1%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=2%2A1-3%2A1%5E2-6%2A1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 1 to the 3rd power to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2-3%2A1%5E2-6%2A1%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=2-3%2A1%5E2-6%2A1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2-3%2A1-6%2A1%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=2-3%2A1-6%2A1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 1 to the 2nd power to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2-3-6%2A1%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=2-3-6%2A1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 and 1 to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-1-6%2A1%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=-1-6%2A1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from 2 to get -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-1-6%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=-1-6%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6 and 1 to get 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-7%2B4 ALIGN=MIDDLE  ALT=\"f%281%29=-7%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 6 from -1 to get -7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-3 ALIGN=MIDDLE  ALT=\"f%281%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add -7 and 4 to get -3\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how y is negative)\r<BR>\n" );
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document.write( "Since the sign of y changes from positive to negative as x goes from 0 to 1, this means that there must be a zero in the interval (0,1)\r<BR>\n" );
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document.write( "Conclusion:\r<BR>\n" );
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document.write( "Since we know that there is a zero in the interval (0,1), but it is <b>not</b> a rational zero, this means that the zero must be irrational.\r<BR>\n" );
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document.write( "So there is an irrational zero in the interval (0,1)\r<BR>\n" );
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document.write( "--------------------------\r<BR>\n" );
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document.write( "Now let's use linear interpolation to find the equation of the line that goes through 2 points on the curve\r<BR>\n" );
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document.write( "Since we previously found that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=4 ALIGN=MIDDLE  ALT=\"f%280%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-3 ALIGN=MIDDLE  ALT=\"f%281%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have the two points (0,4) and (1,-3) that lie on the line. \r<BR>\n" );
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document.write( "Now let's find the equation of the line through (0,4) and (1,-3)\r<BR>\n" );
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document.write( "First lets find the slope through the points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<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=-3 ALIGN=MIDDLE  ALT=\"-3\"   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=m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the slope formula (note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_{1},y_{1}\right)\"> is the first point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_{2},y_{2}\right)\"> is the second point (<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=-3 ALIGN=MIDDLE  ALT=\"-3\"   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=m=%28-3-4%29%2F%281-0%29 ALIGN=MIDDLE  ALT=\"m=%28-3-4%29%2F%281-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=-3 ALIGN=MIDDLE  ALT=\"y%5B2%5D=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=4 ALIGN=MIDDLE  ALT=\"y%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=1 ALIGN=MIDDLE  ALT=\"x%5B2%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=0 ALIGN=MIDDLE  ALT=\"x%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (these are the coordinates of given points)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=+-7%2F1 ALIGN=MIDDLE  ALT=\"m=+-7%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3-4 ALIGN=MIDDLE  ALT=\"-3-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Subtract the terms in the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0 ALIGN=MIDDLE  ALT=\"1-0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <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( "  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-7 ALIGN=MIDDLE  ALT=\"m=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "So the slope is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-7 ALIGN=MIDDLE  ALT=\"m=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "------------------------------------------------\r<BR>\n" );
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document.write( "Now let's use the point-slope formula to find the equation of the line:\r<BR>\n" );
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document.write( "------Point-Slope Formula------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\textrm{x_{1},y_{1}}\right)\"> is one of the given points\r<BR>\n" );
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document.write( "So lets use the Point-Slope Formula to find the equation of the line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=%28-7%29%28x-0%29 ALIGN=MIDDLE  ALT=\"y-4=%28-7%29%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-7 ALIGN=MIDDLE  ALT=\"m=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=0 ALIGN=MIDDLE  ALT=\"x%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=4 ALIGN=MIDDLE  ALT=\"y%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values are given)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-7x%2B%28-7%29%280%29 ALIGN=MIDDLE  ALT=\"y-4=-7x%2B%28-7%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <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( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-7x%2B0 ALIGN=MIDDLE  ALT=\"y-4=-7x%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F0 ALIGN=MIDDLE  ALT=\"0%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F0 ALIGN=MIDDLE  ALT=\"0%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   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=-7x%2B0%2B4 ALIGN=MIDDLE  ALT=\"y=-7x%2B0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to  both sides to isolate y\r<BR>\n" );
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document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7x%2B4 ALIGN=MIDDLE  ALT=\"y=-7x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So we have the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7x%2B4 ALIGN=MIDDLE  ALT=\"y=-7x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through (0,4) and (1,-3) which lie on the curve. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-7x%2B4 ALIGN=MIDDLE  ALT=\"0=-7x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=-7x ALIGN=MIDDLE  ALT=\"-4=-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F%28-7%29=x ALIGN=MIDDLE  ALT=\"-4%2F%28-7%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 7 to isolate x\r<BR>\n" );
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document.write( "So our answer is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.571428571428571 ALIGN=MIDDLE  ALT=\"x=0.571428571428571\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the root to two decimal places is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.57 ALIGN=MIDDLE  ALT=\"x=0.57\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );