SOLUTION: Find the distance between the given line 4x - 3y = 12 and 4x - 3y + 8 = 0.

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Question 1186108: Find the distance between the given line 4x - 3y = 12 and 4x - 3y + 8 = 0.
Answer by ikleyn(52781) About Me  (Show Source):
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Find the distance between the given line 4x - 3y = 12 and 4x - 3y + 8 = 0.
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The distance between two parallel lines, given by equations


    ax + by + c = 0

    ax + by + d = 0


is  Q = abs%28c-d%29%2Fsqrt%28a%5E2+%2B+b%5E2%29.    (1)


In this problem,  a= 4, b= -3, c= -12, d= 8;  so, according to the formula (1), the distance between the lines is


    Q = abs%28-12-8%29%2Fsqrt%284%5E2+%2B+%28-3%5E2%29%29 = 20%2Fsqrt%2825%29 = 20%2F5 = 4 units.      ANSWER

Solved.

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Regarding the formula (1), see this Wikipedia article

https://en.wikipedia.org/wiki/Distance_between_two_parallel_lines