



 
Prasanna, Suppose that you start with a line y = mx + b. This line has slope m and yintercept b. A line parallel to it will also have slope m so its equation will by y = mx + c for some number c. You need to determine the number c so that the perpendicular distance between the lines is d. The line through (0, b) that is perpendicular to y = mx + b has slope 1/m so its equation is y = 1/m x + b. I want to find the point P which is intersection of the lines y = mx + c and y = 1/m x + b and then find the value of c that makes the distance between P and (0, b) equal to d. If P is the intersection of y = mx + c and y = 1/m x + b then mx + c = 1/m x + b and hence the xcoordinate of P is
Substitution of this value into y = 1/m x + b yields the ycoordinate of P as
Now that you know the coordinates of P use the distance formula to write the distance between P and I hope this helps,
 


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