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The line through points (m,-9) and (7,m) has a slope of m. What is the value of m?
\n" ); document.write( "The slope of a line joining two given points A(x1,y1) and B(x2,y2) is given by slope =(y2-y1)/(x2-x1) -----(1)
\n" ); document.write( "In the given problem we have A(X1,y1) given by A(m,-9) implying x1=m, y1=-9
\n" ); document.write( "and B(X2,y2) given by B(7,m) implying x2=7, y2=m
\n" ); document.write( "And given slope = m
\n" ); document.write( "Therefore using the formula (1), we have
\n" ); document.write( "m = [m-(-9)]/[7-m]
\n" ); document.write( "m(7-m) = (m+9) [multiplying through out by (7-m)]
\n" ); document.write( "7m-m^2 = m +9
\n" ); document.write( "0 = m^2-7m+m+9
\n" ); document.write( "(taking both the terms from the left to the right, change side then change sign)
\n" ); document.write( "That is 0 = m^2-6m+9
\n" ); document.write( "0= (m-3)^2
\n" ); document.write( "[as (m^2-6m+9) is a perfect square of the form a^2-2ab+b^2
\n" ); document.write( "where here a = m and b=3]
\n" ); document.write( "And (m-3)^2 = 0 implies m=3 (the equation has root 3 occurring twice)
\n" ); document.write( "Answer: m = 3
\n" ); document.write( "Verifiation: The points A(m,-9) and B(7,m) become
\n" ); document.write( "A(3,-9) and B(7,3)
\n" ); document.write( "and the slope of the line through A(3,-9) and B(7,3) by formula (1) is
\n" ); document.write( "[3-(-9)]/(7-3) = (3+9)/4 = 12/4 = 3 = m which is the given slope.
\n" ); document.write( "Hence our answer for m is right\r
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