document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135207>Question 1135207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My math teacher has asked us this one complex question for points, just for fun, but it counts for points.  Can someone help?  I'm so stressed out!\r<BR>\n" );
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document.write( "Consider an equation of a line written in standard form:  4x  -  2y  =  8. Also consider a point (4, 2) that is not on that line.<BR>\n" );
document.write( "(a) Find the equation of the line that is parallel to 4x  -  2y  =  8  and passes through the point ( 4, 2).<BR>\n" );
document.write( "      Write the equation is all four forms: slope-intercept, point-slope, standard, and two-point forms.<BR>\n" );
document.write( "(b) Find the equation of the line that is perpendicular to 4x  -  2y  =  8  and passes through the point ( 4, 2).<BR>\n" );
document.write( "      Write the equation is all four forms: slope-intercept, point-slope, standard, and two-point forms.<BR>\n" );
document.write( "(c) Graph all three lines on the same coordinate axis.<BR>\n" );
document.write( "      For all three lines, graph four (4) points for each line; twelve (12) points and three (3) lines total.<BR>\n" );
document.write( "      The first point is (4, 2), the second point is of your choosing, and the third & fourth points are<BR>\n" );
document.write( "       the two intercepts (vertical and horizontal); note that (4, 2) is not on the original given line so pick another point on the first line. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752776 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To begin with, relax  :-)<BR>\n" );
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document.write( "slope intercept form is<BR>\n" );
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document.write( "y = mx +b, where m is the slope and b is the y axis intercept<BR>\n" );
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document.write( "point slope form is<BR>\n" );
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document.write( "(y-y1) = m(x-x1), m is the slope and the line passes through the point (x1,y1)<BR>\n" );
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document.write( "standard form is<BR>\n" );
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document.write( "ax +by +c = 0, where a, b, c are constants<BR>\n" );
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document.write( "two point form is<BR>\n" );
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document.write( "(x-x1)/(x2-x1) = (y-y1)/(y2-y1), where the two points are (x1,y1) and (x2,y2)<BR>\n" );
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document.write( "1) 4x - 2y = 8 <BR>\n" );
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document.write( "lets write the point slope form of this line<BR>\n" );
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document.write( "-2y = 8 -4x<BR>\n" );
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document.write( "divide both sides of the = by -2<BR>\n" );
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document.write( "2) y = 2x +8<BR>\n" );
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document.write( "a) the line parallel to equation 2 has the same slope<BR>\n" );
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document.write( "3) y = 2x +b<BR>\n" );
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document.write( "we are given the point (4,2) which the parallel line passes through<BR>\n" );
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document.write( "substitute x = 4 and y = 2 in equation 3<BR>\n" );
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document.write( "2 = 2(4) + b<BR>\n" );
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document.write( "2 = 8 +b<BR>\n" );
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document.write( "b = -6<BR>\n" );
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document.write( "slope intercept form is<BR>\n" );
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document.write( "y = 2x -6<BR>\n" );
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document.write( "point slope form is<BR>\n" );
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document.write( "(y-2) = 2(x-4)<BR>\n" );
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document.write( "standard form is<BR>\n" );
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document.write( "2x -y -6 = 0<BR>\n" );
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document.write( "two point form is<BR>\n" );
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document.write( "use the slope intercept form to find the y axis intercept point<BR>\n" );
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document.write( "set x = 0, then<BR>\n" );
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document.write( "y = 2(0) -6 = -6<BR>\n" );
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document.write( "therefore the second point is (0, -6)<BR>\n" );
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document.write( "two points we are using are (4,2) and (0,-6)<BR>\n" );
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document.write( "(x-4)/(0-4) = (y-2)/(-6-2)<BR>\n" );
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document.write( "b) the slope of the perpendicular line to equation 2 is the negative<BR>\n" );
document.write( "reciprocal of equation 2's slope<BR>\n" );
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document.write( "therefore, the slope is -1/2<BR>\n" );
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document.write( "y = -x/2 +b<BR>\n" );
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document.write( "2 = -4/2 +b<BR>\n" );
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document.write( "b = 4<BR>\n" );
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document.write( "slope intercept form is <BR>\n" );
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document.write( "y = -x/2 +4<BR>\n" );
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document.write( "point slope form is<BR>\n" );
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document.write( "(y-2) = -(x-4)/2<BR>\n" );
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document.write( "standard form is<BR>\n" );
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document.write( "x/2 +y -4 = 0<BR>\n" );
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document.write( "the points to use are (4,2) and (0,4)<BR>\n" );
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document.write( "two point form is <BR>\n" );
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document.write( "(x-4)/(0-4) = (y-2)/(4-2)<BR>\n" );
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document.write( "c)  I will use the slope intercept form for the three lines<BR>\n" );
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document.write( "4) y = 2x +8<BR>\n" );
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document.write( "points are (1,10),(2,12),(0,8),(-4,0)<BR>\n" );
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document.write( "5) y = 2x -6<BR>\n" );
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document.write( "points are (4,2),(2,-2),(0,-6),(3,0)<BR>\n" );
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document.write( "6) y = -x/2 +4<BR>\n" );
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document.write( "points are (4,2),(2,5),(0,4),(8,0)<BR>\n" );
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document.write( "here is the graph, red line is equation 4, green line is equation 5, and blue line is equation 6<BR>\n" );
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