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)![]() ![]() ![]() You can put this solution on YOUR website! 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 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |