document.write( "Question 28964: Directions ask: \"Write an equation in slope-intercept form for each line according to the given information\" \r
\n" ); document.write( "\n" ); document.write( "Contains (3,5)
\n" ); document.write( "Is parallel to 5x-2y=10 \n" ); document.write( "
Algebra.Com's Answer #15835 by sdmmadam@yahoo.com(530)\"\" \"About 
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Directions ask: \"Write an equation in slope-intercept form for each line according to the given information\" \r
\n" ); document.write( "\n" ); document.write( "Contains (3,5)
\n" ); document.write( "Is parallel to 5x-2y=10
\n" ); document.write( "
\n" ); document.write( "The given line is 5x-2y=10
\n" ); document.write( "The given point on the required line is P(3,%)
\n" ); document.write( "That is 5x-2y-10 = 0 ----(1)
\n" ); document.write( "Required to find the equation to a line
\n" ); document.write( "that is parallel to the given line and
\n" ); document.write( "that passes through the given point P(3,5)
\n" ); document.write( "Any line parallel to (1) will be of the form:
\n" ); document.write( " 5x-2y+k = 0 ----(2)
\n" ); document.write( "[giving different values to k will give us different lines each parallel to the given line]
\n" ); document.write( "By data P(3,5) is a point on (2)
\n" ); document.write( "Therefore putting x=3 and y=5 in (2)
\n" ); document.write( "5X(3)-2X(5)+k=0
\n" ); document.write( "15-10 +k=0
\n" ); document.write( "5+k=0
\n" ); document.write( "k=-5
\n" ); document.write( "Putting k=-5 in (2) we get our required line
\n" ); document.write( "5x-2y-5=0 ----(*)
\n" ); document.write( "This is the equation to the required line in the general form.
\n" ); document.write( "But we are asked to present it in the slope and y-intercept form.
\n" ); document.write( "5x-5 =2y (keeping the yterm on one side and the other terms on the other side)
\n" ); document.write( "Dividing by 2,we get
\n" ); document.write( "(5/2)x+(-5/2) = y (making the coefficient of y equal to 1)
\n" ); document.write( "That is y = (5/2)x+(-5/2)
\n" ); document.write( "Which is in the slope and y-intercept form.
\n" ); document.write( "Here slope = (5/2) and y - intercept = (-5/2) \r
\n" ); document.write( "\n" ); document.write( "Answer: 5x-2y-5=0 or equivalently y = (5/2)x+(-5/2)
\n" ); document.write( "Verification: Checking for P(3,5)on this line
\n" ); document.write( "LHS =5x-2y-5 = 5X(3)-2X(5)-5=15-10-5 = 15-15 =0 =the RHS.
\n" ); document.write( "Therefore our equation is right
\n" ); document.write( "Note: Any line parallel to a given line Ax+By+C=0
\n" ); document.write( "is taken as Ax+By +D =0
\n" ); document.write( "What is the idea?
\n" ); document.write( "The idea is: lines parallel and so slopes equal.By taking the xterm and the yterm the same we are establishing that the slope = (-A/B) is the same for the parallel lines.
\n" ); document.write( "It is the different values that D takes that fetches different lines(A parallel beam)each parallel to the given line
\n" ); document.write( "Note: When the coefficient of y is 1 on one side,the coefficient of x on the other side is the slope of the line.\r
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