BUSINESS MATHEMATICS & STATISTICS
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y x x y = 1 − or + = 1 b a a b This result is true for all positions of P on the straight line and hence this is the equations of the required line. (V) Equation of the straight line with given shape m and passing through the given point
( x1 , y1 )
Theon of the straight line with a given slope m is
y = mx+c → (1) Here c is unknown. This straight line passes through the point
( x1 , y1 ) . This point has to satisfy
the equation y=mx+c. Substituting the value of c in (1) we get the equation of the line as
y = mx+y1 -mx1 (ie)
y-y1 = m ( x-x1 )
(vi) The equation of the straight line passing through two given points
( x1 , y1 ) and ( x 2 , y 2 )
y-y1 =m ( x-x1 ) → (1) where m is unknown. The slope of the straight line passing thro the points
m=
y1 − y 2 x1 − x 2
( x1 , y1 ) and ( x1 , y1 ) and ( x 2 , y 2 )
is
→ (2)
Substituting (2) in (1), the equation of the required straight line is
y-y1 = (ie)
y1 − y 2 ( x-x1 ) x1 − x 2
y-y1 y1 − y 2 = x-x1 x1 − x 2
(vii) The equation of a straight line in terms of the perpendicular P from the origin to the line and the angle that perpendicular makes with x axis.
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