document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75462>Question 75462</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0134143841/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How to write an equation of a line with the given slope and y-intercept?\r<BR>\n" );
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document.write( "1. m= 3/7  b=-2         2. m=9, b=0    3. m=0,  b=-5\r<BR>\n" );
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document.write( "How to write an equation of a line through the given points\r<BR>\n" );
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document.write( "1. (-1,1) (2,7)   2. (0,-5)(3,-2)  3. (6,11) (3,13)\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 #54317 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to write an equation of a line with the given slope and y-intercept?\r<BR>\n" );
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document.write( "1. m = 3/7  b = -2         2. m = 9, b = 0       3. m = 0,  b =- 5\r<BR>\n" );
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document.write( "SOLUTION:  \r<BR>\n" );
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document.write( "The general equation of the line is given by:  \r<BR>\n" );
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document.write( "y = mx + b     ----------------(1) represents the standard(general)equation.\r<BR>\n" );
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document.write( "where, m = represents the slope and b represents the y-intercept\r<BR>\n" );
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document.write( "1) m = 3/7  b = -2\r<BR>\n" );
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document.write( "Substituting these in the above equation, we have: \r<BR>\n" );
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document.write( "y = (3/7)x +(-2) \r<BR>\n" );
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document.write( "==> 7y = 3x - 14 \r<BR>\n" );
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document.write( "-------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "2. m = 9, b = 0 \r<BR>\n" );
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document.write( "Substituting these values in the general eqn, we have: \r<BR>\n" );
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document.write( "y = (9)x + 0 \r<BR>\n" );
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document.write( "==> y = 9x \r<BR>\n" );
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document.write( "3. m = 0,  b =- 5\r<BR>\n" );
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document.write( "Substituting these values, we get: \r<BR>\n" );
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document.write( "y = (0)x + (-5)  \r<BR>\n" );
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document.write( "==> y = - 5 \r<BR>\n" );
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document.write( "------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "(II) How to write an equation of a line through the given points\r<BR>\n" );
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document.write( "1. (-1,1) (2,7)   2. (0,-5)(3,-2)  3. (6,11) (3,13) \r<BR>\n" );
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document.write( "Solution:  The equation of the line when two points are given is calculated by using the formula: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+y1%29%2F%28x+-+x1%29+=+%28y2+-+y1%29%2F%28x2+-+x1%29 ALIGN=MIDDLE  ALT=\"%28y+-+y1%29%2F%28x+-+x1%29+=+%28y2+-+y1%29%2F%28x2+-+x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "or this can also be written as : \r<BR>\n" );
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document.write( "(y - y1) = m (x - x1)  ------------------(2)\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+%28y2+-+y1%29%2F%28x2+-+x1%29 ALIGN=MIDDLE  ALT=\"+m+=+%28y2+-+y1%29%2F%28x2+-+x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives the slope of the eqn.\r<BR>\n" );
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document.write( "We first calculate the slope of the eqn and then substitute them in the eqn (2) \r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "1. (-1,1) (2,7) \r<BR>\n" );
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document.write( "Here in this case m  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287+-+1%29%2F%282+-+%28-1%29%29 ALIGN=MIDDLE  ALT=\"%287+-+1%29%2F%282+-+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "               <BR>\n" );
document.write( "              ==> m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F3 ALIGN=MIDDLE  ALT=\"6%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "              ==>  m = 3\r<BR>\n" );
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document.write( "Substituting the point and the slope in the eqn (2), we get: \r<BR>\n" );
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document.write( "y - 1 = 3( x - (-1))\r<BR>\n" );
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document.write( "y - 1 = 3(x + 1) \r<BR>\n" );
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document.write( "y - 1 = 3x + 3 \r<BR>\n" );
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document.write( "y = 3x + 4 \r<BR>\n" );
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document.write( "----------------------------------------------\r<BR>\n" );
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document.write( "2. (0,-5)(3,-2) \r<BR>\n" );
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document.write( "Here in this case m  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2+-%28-5%29%29%2F%283+-+0%29 ALIGN=MIDDLE  ALT=\"%28-2+-%28-5%29%29%2F%283+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "               <BR>\n" );
document.write( "              ==> m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "              ==>  m = 1\r<BR>\n" );
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document.write( "Substituting the point and the slope in the eqn (2), we get: \r<BR>\n" );
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document.write( "y - (-5) = 1( x - 0)\r<BR>\n" );
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document.write( "==> y + 5 = x  is the equation of the straight line.  \r<BR>\n" );
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document.write( "-----------------------------------------------------------------------------\r<BR>\n" );
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document.write( "3. (6,11) (3,13) \r<BR>\n" );
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document.write( "Here in this case the slope of this line is given by: \r<BR>\n" );
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document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813+-+11%29%2F%283+-+6%29 ALIGN=MIDDLE  ALT=\"%2813+-+11%29%2F%283+-+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F-3%29 ALIGN=MIDDLE  ALT=\"%282%2F-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Substituting this in the above formula, we get: \r<BR>\n" );
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document.write( "3y - 33 = -2x + 12 \r<BR>\n" );
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document.write( "3y + 2x = 33 + 12 \r<BR>\n" );
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document.write( "3y + 2x = 45  \r<BR>\n" );
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document.write( "Hence, the solution. \r<BR>\n" );
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document.write( "HAPPY CALCULATING!!!!!  :)) \r<BR>\n" );
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