document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632017>Question 632017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can you help me with this?\r<BR>\n" );
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document.write( "i. Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 3x + 4y -22=0.\r<BR>\n" );
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document.write( "ii. Find an equation of the line passing through (-5, -4) and parallel to the line passing through(-3, 2) and (6, 8).<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 #397967 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=397967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i. Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 3x + 4y -22=0.<BR>\n" );
document.write( "Given<BR>\n" );
document.write( "Point (x, y)=(2,4) <BR>\n" );
document.write( "Line:<BR>\n" );
document.write( "3x+4y-22=0<BR>\n" );
document.write( "Rearrange above equation<BR>\n" );
document.write( "4y=-3x+22<BR>\n" );
document.write( "4y/4=(-3x+22)/4<BR>\n" );
document.write( "y=-3x/4+22/4<BR>\n" );
document.write( "y=(-3/4)x+11/2<BR>\n" );
document.write( "Compare above equation with the equation of line slope-intercept form<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "m=-3/4 and b=11/2<BR>\n" );
document.write( "Slope of the given line m = -3/4 and y-intercept = b = 11/2\r<BR>\n" );
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document.write( "Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (4/3)<BR>\n" );
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document.write( "Now we have a point (2,4) and slope (4/3) of the required required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "4=(4/3)(2)+b<BR>\n" );
document.write( "4=8/3+b<BR>\n" );
document.write( "4-8/3=b<BR>\n" );
document.write( "(12-8)/3=b<BR>\n" );
document.write( "4/3=b<BR>\n" );
document.write( "b=4/3<BR>\n" );
document.write( "y-intercept of the required line =b=4/3<BR>\n" );
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document.write( "Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=(4/3)x-4/3<BR>\n" );
document.write( "Above equation is the required equation of the line in slope-intercept form.\r<BR>\n" );
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document.write( "Graph<BR>\n" );
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document.write( "y=(-3/4)x+11/2<BR>\n" );
document.write( "y=(4/3)x-4/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-3x%2F4%2B11%2F2%2C4x%2F3-4%2F3%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-3x%2F4%2B11%2F2%2C4x%2F3-4%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ii. Find an equation of the line passing through (-5, -4) and parallel to the line passing through(-3, 2) and (6, 8).\r<BR>\n" );
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document.write( "Points  (&#8722;3,2) and (6,8)<BR>\n" );
document.write( "Use point-slope Equation<BR>\n" );
document.write( "m=(y1-y2)/(x1-x2)<BR>\n" );
document.write( "m=(2-8)/(-3-6)<BR>\n" );
document.write( "m=(-6)/(-9)<BR>\n" );
document.write( "m=2/3<BR>\n" );
document.write( "m=2/3 <BR>\n" );
document.write( "Equation of the line Slope-intercept form<BR>\n" );
document.write( "y=mx+b <BR>\n" );
document.write( "Put the value of any one point and slope  in above equation<BR>\n" );
document.write( "m=2/3, Point (-3,2) <BR>\n" );
document.write( "2=(2/3)(-3)+b<BR>\n" );
document.write( "2=-2+b<BR>\n" );
document.write( "2+2=b<BR>\n" );
document.write( "4=b<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "Now<BR>\n" );
document.write( "m=2/3, Point (6,8)<BR>\n" );
document.write( "8=(2/3)(6)+b<BR>\n" );
document.write( "8=(2)(2)+b<BR>\n" );
document.write( "8=4+b<BR>\n" );
document.write( "8-4=b<BR>\n" );
document.write( "4=b<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "b=4 <BR>\n" );
document.write( "Now again put the value of b and m in Equation of the Slope-intercept Form<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=(2/3)x+4<BR>\n" );
document.write( "Above equation is the Equation of the line passing through (-3,2) and (6,8)\r<BR>\n" );
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document.write( "Since the lines are paralallel their slops will be same so slope of the required line is 2/3 and it is passing through the point (-5,-4)<BR>\n" );
document.write( "m=2/3, Point (-5,-4)<BR>\n" );
document.write( "Put the above values in Equation of the line Slope-intercept form<BR>\n" );
document.write( "y=mx+b <BR>\n" );
document.write( "-4=(2/3)(-5)+b<BR>\n" );
document.write( "-4=-10/3+b<BR>\n" );
document.write( "-4+10/3=b<BR>\n" );
document.write( "(-12+10)/3=b<BR>\n" );
document.write( "-2/3=b<BR>\n" );
document.write( "y-intercept of the requaired line b=-2/3<BR>\n" );
document.write( "Put m=2/3 and b=-2/3 in the Equation of the line Slope-intercept form<BR>\n" );
document.write( "y=mx+b <BR>\n" );
document.write( "y=2/3(x)+(-2/3)<BR>\n" );
document.write( "y=2x/3-2/3\r<BR>\n" );
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document.write( "Above equation is the requried equation of the line.<BR>\n" );
document.write( "Graph<BR>\n" );
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document.write( "Line passing through (-3, 2) and (6, 8)<BR>\n" );
document.write( "y=(2/3)x+4<BR>\n" );
document.write( "Line passing through  (-5, -4)<BR>\n" );
document.write( "y=2x/3-2/3<BR>\n" );
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