# Illustration 3 The line L is given by 2x + by = 7, passes through (8,3). The line K is parallel to L and has equation cx + 2y =c. Find the distance between L and K

The line L is given by 2x + by = 7,

passes through (8,3)

2*8+b*3=7

b=-3

2*x-3y=7

K has equation cx + 2y =c

The line K is parallel to L so equation of L and K is only diifer by intercept so value of coeffcient of x, y are same

equation of line L has y coeffiecient of y as -3  while  line K has y coeffiecient of y as 2  so to make them equal ,multiply  eqation of line K by (-3/2)

Equation of Line K becomes

If you equate coefficient of x from eqaution of Line L and K

Equation of K becomes 2*x-3y=2

The distance between L and K is difference of interecept = 7-2=5 unit

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