document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006309>Question 1006309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x) is a linear function, what is the value of n?<BR>\n" );
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document.write( "x     f(x)\r<BR>\n" );
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document.write( "–4     -25<BR>\n" );
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document.write( "-1    -10 \r<BR>\n" );
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document.write( "n    20\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622467 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=622467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1) Find the slope of the line through the two points (-4,-25) and (-1,-10)\r<BR>\n" );
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document.write( "First point (first row of table): <BR>\n" );
document.write( "(x1,y1) = (-4,-25)\r<BR>\n" );
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document.write( "Second point (second row of table): <BR>\n" );
document.write( "(x1,y1) = (-1,-10)\r<BR>\n" );
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document.write( "Slope formula<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (-10 - (-25))/(-1 - (-4))<BR>\n" );
document.write( "m = (-10 + 25)/(-1 + 4)<BR>\n" );
document.write( "m = (15)/(3)<BR>\n" );
document.write( "m = 5\r<BR>\n" );
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document.write( "The slope is m = 5\r<BR>\n" );
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document.write( "Step 2) use y = mx+b, the slope found in step 1, and one of the points to find the value of b\r<BR>\n" );
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document.write( "m = 5<BR>\n" );
document.write( "x = -4<BR>\n" );
document.write( "y = -25\r<BR>\n" );
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document.write( "The x,y pair is found from the first row\r<BR>\n" );
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document.write( "y = mx+b<BR>\n" );
document.write( "y = 5x+b ... replace m with 5<BR>\n" );
document.write( "y = 5(-4)+b ... replace x with -4<BR>\n" );
document.write( "-25 = 5(-4)+b ... replace y with -25; solve for b<BR>\n" );
document.write( "-25 = -20+b<BR>\n" );
document.write( "-25 = b-20<BR>\n" );
document.write( "-25+20 = b-20+20<BR>\n" );
document.write( "-5 = b<BR>\n" );
document.write( "b = -5\r<BR>\n" );
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document.write( "The y intercept is b = -5\r<BR>\n" );
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document.write( "Step 3) Form the equation/function\r<BR>\n" );
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document.write( "We found that the slope is m = 5 and the y intercept is b = -5\r<BR>\n" );
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document.write( "So y = mx+b turns into y = 5x - 5\r<BR>\n" );
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document.write( "Now replace y with f(x) to get f(x) = 5x - 5\r<BR>\n" );
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document.write( "Step 4) Use f(x) = 20 to find the value of x\r<BR>\n" );
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document.write( "f(x) = 5x - 5<BR>\n" );
document.write( "20 = 5x - 5 ... replace f(x) with 20; solve for x<BR>\n" );
document.write( "20+5 = 5x - 5+5<BR>\n" );
document.write( "25 = 5x<BR>\n" );
document.write( "5x = 25<BR>\n" );
document.write( "5x/5 = 25/5<BR>\n" );
document.write( "x = 5\r<BR>\n" );
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document.write( "The input x value of x = 5 produces the output f(x) value of 20\r<BR>\n" );
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document.write( "So n = 5\r<BR>\n" );
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document.write( "Final Answer: <font size = 5 color=red>n = 5</font> </SPAN>\n" );
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