Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14. Find the equation of the second line.

Answer :

We know if we have two parallel lines a_{1}*x* + b_{1}*y* + c_{1} = 0 And a_{2}*x* + b_{2}*y* + c_{2} = 0 , Then the value of all cofficient are As :

$\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\ne \frac{{c}_{1}}{{c}_{2}}$

Here we have a line 4*x* + 3*y* = 14 , So a_{1} = 4 , b_{1} = 3 and c_{1} = - 14

let our line that is parallel to given line is a_{2}*x* + b_{2}*y* + c_{2} = 0 , So

We get

$\frac{4}{{a}_{2}}=\frac{3}{{b}_{2}}\ne \frac{-14}{{c}_{2}}$

So,

a_{2} : b_{2} = 4k : 3k ( Where k is a ratio constant that could be any integer )

So,

We can form any equation that has the co efficients in the ratios 4k : 3k : n (where n is any integer and n$\ne $ 14k)

So,

Our parallel equation could be

**8 x + 6y**

**= 12 ( Ans )**

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