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\n" ); document.write( "Any line parallel to 9x+5y=66 will have an equation of the form 9x+5y=C, where C is some constant; any line perpendicular to 9x+5y=66 will have an equation of the form 5x-9y=C (switch the coefficients and change the sign of one of them).
\n" ); document.write( "So in your problem, an equation of the line you want is 5x-9y=C; the constant C is determined by using the coordinates of the given point.
\n" ); document.write( "5(-6)-9(8) = -30-72 = -102
\n" ); document.write( "An equation of the line you are looking for is
\n" ); document.write( "5x-9y = -102
\n" ); document.write( "In slope-intercept form....
\n" ); document.write( "9y = 5x+102
\n" ); document.write( "y = (5/9)x + 102/9
\n" ); document.write( "or
\n" ); document.write( "y = (5/9)x + 34/3
\n" ); document.write( "If you are supposed to find the solution using basic algebra, then
\n" ); document.write( "(1) put the given equation in slope-intercept form to find its slope;
\n" ); document.write( "(2) find the slope of the line perpendicular to the given line; and
\n" ); document.write( "(3) use the given point to find the y-intercept
\n" ); document.write( "(1)...
\n" ); document.write( "9x+5y = 66
\n" ); document.write( "5y = -9x+66
\n" ); document.write( "y = (-9/5)x+66/5
\n" ); document.write( "(2)... the perpendicular slope is 5/9, the equation is y=(5/9)x+C
\n" ); document.write( "(3)...
\n" ); document.write( "8 = (5/9)(-6)+C
\n" ); document.write( "8 = -10/3+C
\n" ); document.write( "C = 8+10/3 = 34/3
\n" ); document.write( "The equation (as found earlier by the other method) is
\n" ); document.write( "y = (5/9)x + 34/3
\n" ); document.write( " \n" ); document.write( "