document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466443>Question 466443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's the equation of the given lines in standard form?? Help Been stuck for hours\r<BR>\n" );
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document.write( "). The line with m = 4 and intersecting 2x -4y = 8 at x = 6.\r<BR>\n" );
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document.write( "2.) The line through (2, -1) and parallel to x - 2y = 6.\r<BR>\n" );
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document.write( "3.) The line with m = 4 and the point (0, -9).\r<BR>\n" );
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document.write( "4.)The line with a slope of -1/3 and b of 6.\r<BR>\n" );
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document.write( "5.)The line including two points (6, 4) and (-5, 3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319783 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Standard form of equation of a line:<BR>\n" );
document.write( "Ax + By = C<BR>\n" );
document.write( "Slope-intercept form of equation of a line:<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "Point slope form of equation of a line:<BR>\n" );
document.write( "(y - y1) = m(x - x1)\r<BR>\n" );
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document.write( "1) *************************************************<BR>\n" );
document.write( "m = 4<BR>\n" );
document.write( "Now we need a point on the line, the point where the 2 lines intersect at x=6<BR>\n" );
document.write( "To find y value, substitute in 6 for x and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%286%29+-+4y+=+8 ALIGN=MIDDLE  ALT=\"2%286%29+-+4y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+-4y+=+8 ALIGN=MIDDLE  ALT=\"12+-4y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 12 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y+=+-4 ALIGN=MIDDLE  ALT=\"-4y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide by -4 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1 ALIGN=MIDDLE  ALT=\"y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thus the point is (6,1)<BR>\n" );
document.write( "We have slope and a point, use point-slope form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1+=+4%28x-6%29 ALIGN=MIDDLE  ALT=\"y-1+=+4%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1+=+4x+-24 ALIGN=MIDDLE  ALT=\"y-1+=+4x+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 4x on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%2By+-1+=+-24 ALIGN=MIDDLE  ALT=\"-4x+%2By+-1+=+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 1 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%2B+y+=+-23 ALIGN=MIDDLE  ALT=\"-4x+%2B+y+=+-23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation of the line in standard form\r<BR>\n" );
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document.write( "2)***********************************************************<BR>\n" );
document.write( "Parallel lines have equal slopes<BR>\n" );
document.write( "Convert line x - 2y = 6 to slope-intercept form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+2y+=+6 ALIGN=MIDDLE  ALT=\"x+-+2y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract x on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y+=+-x+%2B6 ALIGN=MIDDLE  ALT=\"-2y+=+-x+%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide by -2 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2F2+-+3 ALIGN=MIDDLE  ALT=\"y+=+x%2F2+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From y=mx +b we see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F2 ALIGN=MIDDLE  ALT=\"m=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Point on the line is (2,-1)<BR>\n" );
document.write( "We have slope and a point, use point-slope form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1+=+%281%2F2%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y%2B1+=+%281%2F2%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1+=+x%2F2+-+1 ALIGN=MIDDLE  ALT=\"y%2B1+=+x%2F2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract x/2 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2F2+%2B+y+%2B1+=+-1 ALIGN=MIDDLE  ALT=\"-x%2F2+%2B+y+%2B1+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 1 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2F2+%2B+y+=+-2 ALIGN=MIDDLE  ALT=\"-x%2F2+%2B+y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cannot have fractions in standard form<BR>\n" );
document.write( "Multiply equation by 2 to cancel denominators<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+2y+=+-4 ALIGN=MIDDLE  ALT=\"-x+%2B+2y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation of the line in standard form\r<BR>\n" );
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document.write( "3)*******************************************************<BR>\n" );
document.write( "m = 4<BR>\n" );
document.write( "point on the line is (0,-9)<BR>\n" );
document.write( "We have slope and a point, use point-slope form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+9+=+4%28x+-+0%29 ALIGN=MIDDLE  ALT=\"y+%2B+9+=+4%28x+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B9+=+4x ALIGN=MIDDLE  ALT=\"y%2B9+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 4x on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%2By+%2B9+=+0 ALIGN=MIDDLE  ALT=\"-4x+%2By+%2B9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 9 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%2B+y+=+-9 ALIGN=MIDDLE  ALT=\"-4x+%2B+y+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation of the line in standard form\r<BR>\n" );
document.write( "\n" );
document.write( "4)**********************************************************<BR>\n" );
document.write( "slope = m = -1/3<BR>\n" );
document.write( "y_intercept = b = 6<BR>\n" );
document.write( "We have slope and y_intercept, use slope-intercept form:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%28x%2F3%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+-%28x%2F3%29+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add x/3 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F3%29%2By+=+6 ALIGN=MIDDLE  ALT=\"%28x%2F3%29%2By+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cannot have fractions in standard form<BR>\n" );
document.write( "Multiply equation by 3 to cancel out denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3y+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+3y+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation of the line in standard form\r<BR>\n" );
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document.write( "5) **********************************************************<BR>\n" );
document.write( "Given 2 points (6,4) and (-5,3)<BR>\n" );
document.write( "Find slope using slope formula:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%283-4%29%2F%28-5-6%29 ALIGN=MIDDLE  ALT=\"m+=+%283-4%29%2F%28-5-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-1%29%2F-11 ALIGN=MIDDLE  ALT=\"m+=+%28-1%29%2F-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Division of 2 negative numbers equals a positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1%2F11 ALIGN=MIDDLE  ALT=\"m+=+1%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Pick one of our points, say (6,4)<BR>\n" );
document.write( "We have slope and a point, use point-slope form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4+=+%281%2F11%29%28x-6%29 ALIGN=MIDDLE  ALT=\"y-4+=+%281%2F11%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+-4+=+%28x%2F11%29+-+6%2F11 ALIGN=MIDDLE  ALT=\"+y+-4+=+%28x%2F11%29+-+6%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract x/11 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%2F11%29+%2B+y+-4+=+-6%2F11 ALIGN=MIDDLE  ALT=\"-%28x%2F11%29+%2B+y+-4+=+-6%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 4 on both sides<BR>\n" );
document.write( "Notice we have to add fractions, find common denominator<BR>\n" );
document.write( "4 = 44/11<BR>\n" );
document.write( "-6/11 + 44/11 = 38/11<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%2F11%29+%2B+y+=+38%2F11 ALIGN=MIDDLE  ALT=\"-%28x%2F11%29+%2B+y+=+38%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cannot have fractions in standard form<BR>\n" );
document.write( "Multiply equation by 11 to cancel out denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+11y+=+38 ALIGN=MIDDLE  ALT=\"-x+%2B+11y+=+38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation of the line in standard form\r<BR>\n" );
document.write( "\n" );
document.write( "******************************************************<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );