document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=822037>Question 822037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was confused on how you solve this question. The question states: write an equation for the linear function f with the given values. f(6)=-4, f(9)=-9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494559 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=494559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You know equations representing a line that can be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > with some constants <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You can think of those equations as linear functions with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > being a function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You could write them as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=mx%2Bb ALIGN=MIDDLE  ALT=\"f%28x%29=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the type of equation you need to find.<BR>\n" );
document.write( "There's more than one way to the answer.<BR>\n" );
document.write( "You could substitute the values given and solve the resulting system of equations for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You could also draw on what you know of equations of a line,<BR>\n" );
document.write( "figure out the slope,<BR>\n" );
document.write( "use one point to write the equation in point-slope form,<BR>\n" );
document.write( "and then solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the slope-intercept form of the equation.<BR>\n" );
document.write( " <BR>\n" );
document.write( "SOLVING A SYSTEM:<BR>\n" );
document.write( "We substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%286%29=-4 ALIGN=MIDDLE  ALT=\"f%286%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%289%29=-9 ALIGN=MIDDLE  ALT=\"f%289%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=mx%2Bb ALIGN=MIDDLE  ALT=\"f%28x%29=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get two equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-4=6m%2Bb%2C-9=9m%2Bb%29 ALIGN=MIDDLE  ALT=\"system%28-4=6m%2Bb%2C-9=9m%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting the first equation from the second, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2B4=9m-6m ALIGN=MIDDLE  ALT=\"-9%2B4=9m-6m\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5=3m ALIGN=MIDDLE  ALT=\"-5=3m\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F3 ALIGN=MIDDLE  ALT=\"m=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting that value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=6%2A%28-5%2F3%29%2Bb ALIGN=MIDDLE  ALT=\"-4=6%2A%28-5%2F3%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=-10%2Bb ALIGN=MIDDLE  ALT=\"-4=-10%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2B10=b ALIGN=MIDDLE  ALT=\"-4%2B10=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the linear function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=%28-5%2F3%29x%2B6%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=%28-5%2F3%29x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "FINDING THE EQUATION OF A LINE:<BR>\n" );
document.write( "The information given, tells you that<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <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;\" >  so point (6,-4) is on the line,<BR>\n" );
document.write( "and it also tells you that<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-9 ALIGN=MIDDLE  ALT=\"y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  so point (9,-9) is on the line.<BR>\n" );
document.write( "The slope is the difference in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > values divided by the difference in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-9-%28-4%29%29%2F%289-6%29=%28-9%2B4%29%2F3=-5%2F3 ALIGN=MIDDLE  ALT=\"m=%28-9-%28-4%29%29%2F%289-6%29=%28-9%2B4%29%2F3=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With that slope and knowing that the line goes through (6,-4) we can write a point-slope form of the equation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-4%29=%28-5%2F3%29%28x-6%29 ALIGN=MIDDLE  ALT=\"y-%28-4%29=%28-5%2F3%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=%28-5%2F3%29%28x-6%29 ALIGN=MIDDLE  ALT=\"y%2B4=%28-5%2F3%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%7D%7D+to+get+the+slope-intercept+form%3A%0D%0A%7B%7B%7By%2B4=%28-5%2F3%29%28x-6%29 ALIGN=MIDDLE  ALT=\"y%7D%7D+to+get+the+slope-intercept+form%3A%0D%0A%7B%7B%7By%2B4=%28-5%2F3%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=%28-5%2F3%29x-6%28-5%2F3%29 ALIGN=MIDDLE  ALT=\"y%2B4=%28-5%2F3%29x-6%28-5%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=%28-5%2F3%29x%2B10 ALIGN=MIDDLE  ALT=\"y%2B4=%28-5%2F3%29x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29x%2B10-4 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29x%2B10-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F3%29x%2B6 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you would write it with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead 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;\" > , as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=%28-5%2F3%29x%2B6%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=%28-5%2F3%29x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );