document.write( "Question 30494: Find the equation, in standard form, of the line that passes through the points (5,6) and (7, 3) \n" ); document.write( "
Algebra.Com's Answer #17162 by sdmmadam@yahoo.com(530)\"\" \"About 
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Find the equation, in standard form, of the line that passes through the points (5,6) and (7, 3)
\n" ); document.write( "Given two points P(x1,y1) and Q(x2,y2) on a given line
\n" ); document.write( "the equation to the given line is
\n" ); document.write( "(y-y1)/(y1-y2) = (x-x1)/(x1-x2)----(1)
\n" ); document.write( "Therefore given two points P(5,6) and Q(7, 3),
\n" ); document.write( "the equation to the line passing through P and Q is
\n" ); document.write( "(here x1 = 5, y1 = 6; x2 = 7, y2 = 3 )
\n" ); document.write( "(y-6)/(6-3) = (x-5)/(5-7)
\n" ); document.write( "That is (y-6)/3 = (x-5)/(-2)
\n" ); document.write( "Multiplying by 6 on both the sides (since lcm of 3 and 2 is 6)
\n" ); document.write( "2(y-6) = -3(x-5)
\n" ); document.write( "2y-12 = -3x+15
\n" ); document.write( "3x+2y-12-15 = 0 (grouping like terms,changing sign while changing side)
\n" ); document.write( "3x+2y-27 =0 ----(*)
\n" ); document.write( "which is the equation to the line in the general form
\n" ); document.write( "If by standard form you mean the slope and the y-intercept form
\n" ); document.write( "retain the y-term on the left side and take the other terms to the right
\n" ); document.write( "and then divide by the coefficient 2 of y
\n" ); document.write( "then the slope and y-intercept form of the required line is
\n" ); document.write( "y = (-3/2)x +(27/2) ----(**)
\n" ); document.write( "Verification: Testing for P(5,6) and Q(7, 3)in (*)
\n" ); document.write( "LHS = 3x+2y-27
\n" ); document.write( "= 3X(5)+2X(6)-27 (putting x = 5 and y = 6 in (1) )
\n" ); document.write( "= 13+12-27
\n" ); document.write( "= 27-27
\n" ); document.write( "= 0
\n" ); document.write( "=RHS
\n" ); document.write( "P(5,6) is a point on (*)\r
\n" ); document.write( "\n" ); document.write( "Now putting x = 7 and y = 3 in (*)
\n" ); document.write( "that is checking if Q(7,3) is a point on (*)
\n" ); document.write( "LHS = 3x+2y-27
\n" ); document.write( "= 3X(7)+2X(3)-27
\n" ); document.write( "= 21+6-27
\n" ); document.write( "= 27-27
\n" ); document.write( "= 0
\n" ); document.write( "=RHS
\n" ); document.write( "This implies Q(7,3) is a point on (*)\r
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