Question 704164: Write equation in standard form of the line through the given points.
(-2/5, 2/5) and (4/3, 2/3)
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Given the standard form
(1) Ax + By = C
Substiute the point (-2/5,2/5) into (1) and get
(2) A*(-2/5) + B*(2/5) = C
Simplify (2) by multiplying both sides by 5 and get
(3) -2*A + 2*B = 5*C
Substitute the point (4/3,2/3) into (1) and get
(4) A*(4/3) +B*(2/3) = C
Simplify (4) by multiplying both sides by 3 and get
(5) 4*A + 2*B = 3*C
Now subtract (3) from (5) and get
(6) 6*A = -2*C or
(7) A = -(1/3)*C
Now add 2*(3) to (5) and get
(8) 6*B = 13*C or
(9) B = (13/6)*C
Now substitute A and B of (7) and (9) into (1) and get
(10) -(1/3)*C*x + (13/6)*C*y = C
Note that all terms have the common factor, C, and can be cancelled to get
(11) -(1/3)x + (13/6)*y = 1
Now multiple both sides by 6 to get
(12) -2*x + 13*y = 6
Use the two given points to check (12).
Is (-2*(-2/5) + 13*(2/5) = 6)?
Is ((4 + 26)/5 = 6)?
Is (30/5 = 6)?
Is (6 = 6)? Yes
Is ( -2*(4/3) + 13*(2/3) = 6)?
Is ((-8 + 26)/3 = 6)?
Is (18/3 = 6)?
Is (6 = 6)? Yes
Answer: In standard form, the line that passes through the two given points is
-2x + 13y = 6.
PS You can simplify the above by defining new variables A/C and B/C.
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