document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631910>Question 631910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line perpendicular to 4x-5y=3 through (2,3).<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 #397948 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=397948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given<BR>\n" );
document.write( "Point (x, y)=(2,3) <BR>\n" );
document.write( "Line:<BR>\n" );
document.write( "4x-5y=3<BR>\n" );
document.write( "-5y=-4x+3<BR>\n" );
document.write( "-5y/-5=(-4x+3)/-5<BR>\n" );
document.write( "y=-4x/-5-3/5<BR>\n" );
document.write( "y=(4/5)x-3/5<BR>\n" );
document.write( "Compare above equation with the equation of line slope-intercept form<BR>\n" );
document.write( "y=mx+b\r<BR>\n" );
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document.write( "m=4/5 and b=-3/5<BR>\n" );
document.write( "Slope of the given line m = 4/5 and y-intercept = b = -3/5\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 (-5/4)<BR>\n" );
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document.write( "Now we have a point (2,3) and slope (-5/4) of the 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( "3=(-5/4)(2)+b<BR>\n" );
document.write( "3=-10/4+b<BR>\n" );
document.write( "3+10/4=b<BR>\n" );
document.write( "(12+10)/4=b<BR>\n" );
document.write( "22/4=b<BR>\n" );
document.write( "11/2=b<BR>\n" );
document.write( "b=11/2<BR>\n" );
document.write( "y-intercept of the required line = b = 11/2 and slope = m = -5/4<BR>\n" );
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=(-5/4)x+11/2<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=(4/5)x-3/5 (Given line)<BR>\n" );
document.write( "y=(-5/4)x+11/2(Required line)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4x%2F5-3%2F5%2C-5x%2F4%2B11%2F2%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4x%2F5-3%2F5%2C-5x%2F4%2B11%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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