document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005035>Question 1005035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation for a linear function f that has the given values f(-3) =2 and f(1)=0<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 #621356 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the slope intercept form of the linear function is:\r<BR>\n" );
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document.write( "y = mx + b\r<BR>\n" );
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document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept\r<BR>\n" );
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document.write( "m = (y2-y1) / (x2-x1)\r<BR>\n" );
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document.write( "(x1,y1) is any one point on the line.<BR>\n" );
document.write( "(x2,y2) is any other point on the line.\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "f(1) = 0<BR>\n" );
document.write( "f(-3) = 2\r<BR>\n" );
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document.write( "f(1) = 0 means that the value of the function is equal to 0 when the value of x is equal to 1.\r<BR>\n" );
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document.write( "that tells you that your first point will be (x1,y1) = (1,0)\r<BR>\n" );
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document.write( "f(-3) = 2 means that the value of the function is equal to 2 when the value of x is equal to -3.\r<BR>\n" );
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document.write( "that tells you that your second pont will be (x2,y2) = -3,2)\r<BR>\n" );
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document.write( "now that you have two points on the line, you can find the slope.\r<BR>\n" );
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document.write( "m = (y2 - y1) / (x2 - x1) which becomes:\r<BR>\n" );
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document.write( "m = (2 - 0) / (-3 - 1) which becomes:\r<BR>\n" );
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document.write( "m = 2 / -4 which becomes:\r<BR>\n" );
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document.write( "m = -1/2\r<BR>\n" );
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document.write( "you now have your slope.\r<BR>\n" );
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document.write( "the general form of the equation of y = mx + b becomes:\r<BR>\n" );
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document.write( "y = -(1/2)x + b\r<BR>\n" );
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document.write( "all that's left is to find b, which is the y-intercept.\r<BR>\n" );
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document.write( "take any one of your known points and replace y with the y value of the coordinate and replace x with the x value of the coordinate and solve for b.\r<BR>\n" );
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document.write( "we'll use (x2,y2) = (-3,2)\r<BR>\n" );
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document.write( "your equation is y = -(1/2)x + b\r<BR>\n" );
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document.write( "replace y with 2 and replace x with -3 and the equation becomes:\r<BR>\n" );
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document.write( "2 = -(1/2)*(-3) + b\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "2 = (3/2) + b\r<BR>\n" );
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document.write( "subtract (3/2) from both sides of the equation to get:\r<BR>\n" );
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document.write( "2 - (3/2) = b\r<BR>\n" );
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document.write( "solve for b to get:\r<BR>\n" );
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document.write( "b = 1/2\r<BR>\n" );
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document.write( "your equation is now:\r<BR>\n" );
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document.write( "y = -(1/2)x + 1/2\r<BR>\n" );
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document.write( "you're done.\r<BR>\n" );
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document.write( "y = -(1/2)x + 1/2 is the same as:\r<BR>\n" );
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document.write( "f(x) = -(1/2)x + 1/2, if you set y = f(x).\r<BR>\n" );
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document.write( "when the value of x is equal to 1, your function becomes:\r<BR>\n" );
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document.write( "f(1) = -(1/2)*1 + 1/2 which becomes:\r<BR>\n" );
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document.write( "f(1) = -1/2 + 1/2 which becomes:\r<BR>\n" );
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document.write( "f(1) = 0\r<BR>\n" );
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document.write( "when the value of x is equal to -3, your function becomes:\r<BR>\n" );
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document.write( "f(-3) = -(1/2)*(-3) + 1/2 which becomes:\r<BR>\n" );
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document.write( "f(-3) = (3/2) + 1/2 which becomes:\r<BR>\n" );
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document.write( "f(-3) = 2\r<BR>\n" );
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document.write( "the equation is modelling the straight line that goes through both your given points.\r<BR>\n" );
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