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Equation of the line slope-intercept form
\n" ); document.write( "y=mx+b
\n" ); document.write( "Given
\n" ); document.write( "Equation of the Given line
\n" ); document.write( "2x-3y=6
\n" ); document.write( "-3y=-2x+6
\n" ); document.write( "-3y/-3=(-2x+6)/-3
\n" ); document.write( "y=2x/3-2
\n" ); document.write( "y=(2/3)x-2
\n" ); document.write( "Compare with the equation of line slope-intercept form
\n" ); document.write( "Slope of the given = m = 2/3
\n" ); document.write( "Since lines are parallel their slope will be same
\n" ); document.write( "Slope of the required line = m = 2/3
\n" ); document.write( "Point (0, 1)
\n" ); document.write( "We have a point and slope we can get easily the require line equation.
\n" ); document.write( "Use Equation of the line point-slope form
\n" ); document.write( "m = y2-y1/x2-x1
\n" ); document.write( "Put the values in above equation, we have
\n" ); document.write( "2/3=(y-1)/(x-0)
\n" ); document.write( "2/3=(y-1)/x
\n" ); document.write( "2x=3(y-1)
\n" ); document.write( "2x=3y-3
\n" ); document.write( "-3y=-2x-3
\n" ); document.write( "-3y/-3=-(2x+3)/-3
\n" ); document.write( "y=2x/3+3/3
\n" ); document.write( "y=(2/3)x+1
\n" ); document.write( "Above equation is the equation of the required line\r
\n" ); document.write( "\n" ); document.write( "Graph
\n" ); document.write( "=====
\n" ); document.write( "y=(2/3)x-2 (Given line in green)
\n" ); document.write( "y=(2/3)x+1 (Required line in Red)
\n" ); document.write( "