document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146541>Question 146541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please write the linear function for which f (3) =6 and f (-4) =2\r<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 #106974 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=106974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f (3) =6 tells us that when x=3, then y=6. So we know that the equation goes through the point (3,6)\r<BR>\n" );
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document.write( "f (-4) =2 tells us that when x=-4, then y=2. So we know that the equation goes through the point (-4,2)\r<BR>\n" );
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document.write( "So let's find the equation of the line that goes through the points (3,6) and (-4,2)\r<BR>\n" );
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document.write( "First let's find the slope through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,6\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-4,2\right)\">\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.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%282-6%29%2F%28-4-3%29 ALIGN=MIDDLE  ALT=\"m=%282-6%29%2F%28-4-3%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=2 ALIGN=MIDDLE  ALT=\"y%5B2%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=6 ALIGN=MIDDLE  ALT=\"y%5B1%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-4 ALIGN=MIDDLE  ALT=\"x%5B2%5D=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=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=%28-4%29%2F%28-4-3%29 ALIGN=MIDDLE  ALT=\"m=%28-4%29%2F%28-4-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-4%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"m=%28-4%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <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=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=4%2F7 ALIGN=MIDDLE  ALT=\"m=4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the slope of the line that goes through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,6\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-4,2\right)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4%2F7 ALIGN=MIDDLE  ALT=\"m=4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's use the point slope formula:\r<BR>\n" );
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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;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%284%2F7%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y-6=%284%2F7%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4%2F7 ALIGN=MIDDLE  ALT=\"m=4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=6 ALIGN=MIDDLE  ALT=\"y%5B1%5D=6\"   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-6=%284%2F7%29x%2B%284%2F7%29%28-3%29 ALIGN=MIDDLE  ALT=\"y-6=%284%2F7%29x%2B%284%2F7%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=%284%2F7%29x-12%2F7 ALIGN=MIDDLE  ALT=\"y-6=%284%2F7%29x-12%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F7%29x-12%2F7%2B6 ALIGN=MIDDLE  ALT=\"y=%284%2F7%29x-12%2F7%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 6 to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F7%29x%2B30%2F7 ALIGN=MIDDLE  ALT=\"y=%284%2F7%29x%2B30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. note: If you need help with fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a>.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F7%29x%2B30%2F7 ALIGN=MIDDLE  ALT=\"y=%284%2F7%29x%2B30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So the equation that goes through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,6\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-4,2\right)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F7%29x%2B30%2F7 ALIGN=MIDDLE  ALT=\"y=%284%2F7%29x%2B30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Notice how the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F7%29x%2B30%2F7 ALIGN=MIDDLE  ALT=\"y=%284%2F7%29x%2B30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,6\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-4,2\right)\">. So this visually verifies our answer.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=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%284%2F7%29x%2B30%2F7%29%2C%0D%0A+circle%283%2C6%2C0.08%29%2C%0D%0A+circle%283%2C6%2C0.10%29%2C%0D%0A+circle%283%2C6%2C0.12%29%2C%0D%0A+circle%28-4%2C2%2C0.08%29%2C%0D%0A+circle%28-4%2C2%2C0.10%29%2C%0D%0A+circle%28-4%2C2%2C0.12%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F7%29x%2B30%2F7 ALIGN=MIDDLE  ALT=\"y=%284%2F7%29x%2B30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3,6\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-4,2\right)\">\r<BR>\n" );
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