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Given the standard form
\n" ); document.write( "(1) Ax + By = C
\n" ); document.write( "Substiute the point (-2/5,2/5) into (1) and get
\n" ); document.write( "(2) A*(-2/5) + B*(2/5) = C
\n" ); document.write( "Simplify (2) by multiplying both sides by 5 and get
\n" ); document.write( "(3) -2*A + 2*B = 5*C
\n" ); document.write( "Substitute the point (4/3,2/3) into (1) and get
\n" ); document.write( "(4) A*(4/3) +B*(2/3) = C
\n" ); document.write( "Simplify (4) by multiplying both sides by 3 and get
\n" ); document.write( "(5) 4*A + 2*B = 3*C
\n" ); document.write( "Now subtract (3) from (5) and get
\n" ); document.write( "(6) 6*A = -2*C or
\n" ); document.write( "(7) A = -(1/3)*C
\n" ); document.write( "Now add 2*(3) to (5) and get
\n" ); document.write( "(8) 6*B = 13*C or
\n" ); document.write( "(9) B = (13/6)*C
\n" ); document.write( "Now substitute A and B of (7) and (9) into (1) and get
\n" ); document.write( "(10) -(1/3)*C*x + (13/6)*C*y = C
\n" ); document.write( "Note that all terms have the common factor, C, and can be cancelled to get
\n" ); document.write( "(11) -(1/3)x + (13/6)*y = 1
\n" ); document.write( "Now multiple both sides by 6 to get
\n" ); document.write( "(12) -2*x + 13*y = 6
\n" ); document.write( "Use the two given points to check (12).
\n" ); document.write( "Is (-2*(-2/5) + 13*(2/5) = 6)?
\n" ); document.write( "Is ((4 + 26)/5 = 6)?
\n" ); document.write( "Is (30/5 = 6)?
\n" ); document.write( "Is (6 = 6)? Yes
\n" ); document.write( "Is ( -2*(4/3) + 13*(2/3) = 6)?
\n" ); document.write( "Is ((-8 + 26)/3 = 6)?
\n" ); document.write( "Is (18/3 = 6)?
\n" ); document.write( "Is (6 = 6)? Yes
\n" ); document.write( "Answer: In standard form, the line that passes through the two given points is
\n" ); document.write( " -2x + 13y = 6.
\n" ); document.write( "PS You can simplify the above by defining new variables A/C and B/C. \n" ); document.write( "